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Prepared for submission to JHEP
Two-Loop QCD Correction to massive spin-2
resonance → 3 gluons
Taushif Ahmed,a Maguni Mahakhud,a Prakash Mathews,b Narayan Ranaa and V.
Ravindranc
aHarish-Chandra Research Institute,
Chhatnag Road, Jhunsi, Allahabad 211 019, Uttar Pradesh, IndiabSaha Institute of Nuclear Physics,
1/AF Bidhan Nagar, Kolkata 700 064, IndiacThe Institute of Mathematical Sciences,
C.I.T Campus, 4th Cross St, Tharamani, Chennai 600 113, Tamil Nadu, India
E-mail: taushif@hri.res.in, maguni@hri.res.in,
prakash.mathews@saha.ac.in, narayan@hri.res.in, ravindra@imsc.res.in
Abstract: We present the O(α3s) virtual QCD corrections to the process h→ g+g+g due
to interference of born and two-loop amplitudes, where h is a massive spin-2 particle and g
is the gluon. We assume that the SM fields couple to h through the SM energy momentum
tensor. Our result constitutes one of the ingredients to full NNLO QCD contribution
to production of a massive spin-2 particle along with a jet in the scattering process at
the LHC. In particular, this massive spin-2 could be a KK mode of a ADD graviton in
large extra dimensional model or a RS KK mode in warped extra dimensional model or a
generic massive spin-2. In addition, it provides an opportunity to study the ultraviolet and
infrared structures of QCD amplitudes involving tensorial coupling resulting from energy
momentum operator. Using dimensional regularization, we find that infrared poles of
this amplitude are in agreement with the proposal by Catani confirming the factorization
property of QCD amplitudes with tensorial insertion.
Keywords: QCD, Spin-2 and NNLO calculation
arX
iv:1
404.
0028
v1 [
hep-
ph]
31
Mar
201
4
Contents
1 Introduction 1
2 Theory 3
2.1 The effective Lagrangian 3
2.2 Notation 4
2.3 Ultraviolet renormalization 4
2.4 Infrared factorization 5
3 Calculation of two-loop amplitude 6
3.1 Feynman diagrams and simplification 6
3.2 Reduction of tensor integrals 7
3.3 Master integrals 9
4 Results 10
5 Conclusion 11
A Harmonic polylogarithms 13
B One-loop coefficients 14
C Two-loop coefficients 15
1 Introduction
Theoretical studies on production and decay of a spin JP particle in the hadron colliders
in the Standard Model (SM) and its extensions are underway due to a wealth of informa-
tion available from ATLAS [1] and CMS [2] collaborations at the Large Hadron Collider
(LHC). In particular, investigations involving particles with higher spin, namely JP = 2+
bosons gained attention [3, 4] due to the discovery of a new boson at the LHC with a mass
m ≈ 125 GeV as its spin is yet to be determined with no doubt. Searches of spin-2 particles
earlier in Tevatron and recently in LHC were motivated due to their presence in theories
with large extra dimensions, such as ADD [5] and warped extra dimensions such as RS
[6] models. These beyond the SM (BSM) theories provide an alternate scenario to explain
the hierarchy problem of the SM through the introduction of compact higher dimensions
with factorisable (ADD) or non-factorisable (RS) geometries. The impact of these higher
dimensions can be understood in four dimensional framework through the existence of a
tower of massive spin-2 Kaluza-Klein (KK) gravitons. Their signatures at the colliders
can provide valuable information on these models. For the production of scalar JP = 0+
– 1 –
and vector JP = 1+ particles in the SM and BSM, there are extensive studies available
in literature. They include inclusive and semi-inclusive rates taking into account quantum
chromodynamics (QCD) and electroweak (EW) radiative corrections to impressively high
orders in perturbative expansion. Thanks to universal features of some of the perturbative
corrections in QCD, one can safely use those computed in the SM for BSM processes. For
spin-2 particles, searches in Drell-Yan (DY), di-photon and jet+missing energy at the LHC
are already underway. Also the bounds on the scale of the new physics and the number
of extra-dimensions are severely constrained from these searches. These studies use theo-
retical results computed in QCD at NLO level in perturbation theory. Such computations
are inevitable due to various uncertainties resulting from renormalization and factorization
scales as well as from the parton distribution functions. Needless to say that the correc-
tions are also big giving large K-factors which are often sensitive to the observables and
their physical scales. In ADD and RS models spin-2 KK gravitons contribute to physical
processes through either exchange of virtual graviton state or production of a real graviton
state. In the virtual mode, KK gravitons get exchanged between the SM particles and the
summation over their high multiplicity leads to a compensation of small coupling strength.
Hence, the cross section will be appreciable at collider energies, giving rise to non-resonant
enhancement of the high invariant mass regions of a di-final state production [7–9] or final
states involving more particles [10]. Next to leading order QCD corrections were computed
for the di-final state processes in the ADD model viz. `+`− [11–13], γγ [14, 15] and ZZ
[16, 17] and W+W− [18, 19], in addition they have been extended to NLO+PS accuracy
[20, 21]. On-shell spin-2 particle production results in missing energy signal. Again large
multiplicity of final states enhances the observable effects. Productions of on-shell spin-2
gravitons in association with (a) jet [22], (b) photon [23] and (c) electroweak gauge boson
[24] have been studied to NLO in QCD. Similar results taking into account NLO QCD
effects for processes involving the resonant production of spin-2 graviton are available for
di-lepton production [12, 13], di-photon production [15], di-neutral electroweak gauge bo-
son production [17] and charged electroweak gauge boson production W+W− [19]. Since
the NLO corrections and the associated scale uncertainties are not completely under con-
trol in most of the observable, an attempt [25] was undertaken to include soft and collinear
contribution to NNLO accuracy for processes involving KK gravitons in both ADD and
RS models. This was possible as the full two loop QCD matrix element of energy momen-
tum tensor is now available [26]. The phenomenological results show significant reduction
in dependence on renormalization and factorization scales and these results improve the
stability of the perturbative predictions.
Observables with jet + missing energy are sensitive to new physics from many BSM
scenarios. This missing energy could be due to a heavy resonance produced in the final state
escaping the detector. The NLO QCD effects to this process in large extra dimensional
model, namely ADD have been available for sometime and the importance of K-factor
and scale uncertainties are documented in [22]. In this article, we compute O(α3s) virtual
correction in massless QCD to the process h → g + g + g due to interference of born
and two-loop amplitudes, where h is a massive spin-2 particle. The full NNLO analysis
also requires square of one loop amplitudes, real emission processes and appropriate mass
– 2 –
counter terms which we reserve for future work. We have assumed a minimal coupling
between massive spin-2 field and the fields of the SM. Hence our results are applicable
to scattering processes involving a massive spin-2 particle and three gluons such as a
massive graviton production with a jet in ADD and RS models or production of a massive
spin-2 Higgs like boson along with a jet after appropriate analytical continuation [27] of
kinematical variables to the respective physical regions. Similar computations with massive
spin-0 and spin-1 boson productions at two loop level in QCD exist in the literature for
the processes Higgs→ g + g + g [28] and g + g → V + jet, V = Z, γ [29] respectively.
Spin-2 field being a rank-2 tensor, we encounter for the first time the two loop am-
plitudes with higher tensorial integrals resulting from rank-2 derivative couplings of spin-2
fields with the SM ones. In addition, we encounter more than 2000 two loop Feynman am-
plitudes contributing due to the universal coupling of spin-2 field with all the SM particles.
While these increase technical complexities at the intermediate stages of computation, the
results confirm the universal infra-red structure of QCD amplitudes. In other words, we
find that soft and collinear divergences not only factorise but also agree with the predic-
tions from Catani’s work [30] (see also [31]) on two loop QCD amplitudes for multi-leg
processes. We also observe that there are no additional UV divergences as the interaction
is through energy momentum tensor of the SM which is conserved. Hence, our present
work is also useful to study the field theoretical structure of QCD amplitudes with tensor
operator insertions, in particular with the energy momentum tensor of the SM.
In the next section, we describe the generic effective Lagrangian that describes coupling
of spin-2 fields with those of the SM. Section 3 is devoted to the computational details.
Section 4 and Appendix contain our final results. In section 5, we conclude with our
findings.
2 Theory
2.1 The effective Lagrangian
We consider the SM with an additional spin-2 field hµν . We assume that the spin-2 field
couples minimally with the SM ones through the SM energy momentum tensor TSMµν . Since
we are interested only in the QCD effects of the process under study, we restrict ourselves
to the QCD part of TSMµν and hence the action reads [5, 6] as
S = SSM + Sh −κ
2
∫d4x TQCDµν (x) hµν(x) , (2.1)
where κ is a dimensionful coupling and TQCDµν is the energy momentum tensor of QCD
given by
TQCDµν = −gµνLQCD − F aµρF aρν −1
ξgµν∂
ρ(Aaρ∂σAaσ) +
1
ξ(Aaν∂µ(∂σAaσ) +Aaµ∂ν(∂σAaσ))
+i
4
[ψγµ(
−→∂ ν − igsT aAaν)ψ − ψ(
←−∂ ν + igsT
aAaν)γµψ + ψγν(−→∂ µ − igsT aAaµ)ψ
−ψ(←−∂ µ + igsT
aAaµ)γνψ]
+ ∂µωa(∂νω
a − gsfabcAcνωb)
– 3 –
+∂νωa(∂µω
a − gsfabcAcµωb). (2.2)
gs is the strong coupling constant and ξ is the gauge fixing parameter. The T a are genera-
tors and fabc are the structure constants of SU(3). Note that spin-2 fields couple to ghost
fields (ωa) [32] as well in order to cancel unphysical degrees of freedom of gluon fields (Aaµ).
2.2 Notation
We consider the decay of a massive spin-2 field into three gluons
h(q)→ g(p1) + g(p2) + g(p3). (2.3)
The associated Mandelstam variables are defined as
s ≡ (p1 + p2)2, t ≡ (p2 + p3)
2, u ≡ (p1 + p3)2 (2.4)
which satisfy
s+ t+ u = M2h ≡ Q2 (2.5)
where Mh is the mass of the spin-2 field. We also define the following dimensionless
invariants which appear in harmonic polylogarithms (HPL) [33] and 2dHPL [34, 35] as
x ≡ s/Q2, y ≡ u/Q2, z ≡ t/Q2 (2.6)
satisfying
x+ y + z = 1. (2.7)
2.3 Ultraviolet renormalization
We describe here the ultraviolet (UV) renormalization of the matrix elements of the decay
of a spin-2 resonance with minimal coupling up to second order in QCD perturbation
theory. We regularize the theory in d = 4 + ε dimensions and the dimensionful strong
coupling constant in d dimensions is made dimensionless one (gs) by introducing the scale
µ0. We expand the unrenormalized amplitude in powers of as = g2s/16π2 as
|M〉 =
(asµε0Sε
) 12
|M(0)〉+
(asµε0Sε
) 32
|M(1)〉+
(asµε0Sε
) 52
|M(2)〉+O(a3s) , (2.8)
where Sε = exp[ ε2(γE − ln 4π)] with Euler constant γE = 0.5772 . . . , results from loop
integrals beyond leading order. |M(i)〉 is the unrenormalized color-space vector representing
the ith loop amplitude. In MS scheme, the renormalized coupling constant as ≡ as(µ2R) at
renormalization scale µR is related to unrenormalized coupling constant as by
asµε0Sε =
asµεR
Z(µ2R)
=asµεR
[1 + as
2β0ε
+ a2s
(4β20ε2
+β1ε
)+O(a3s)
], (2.9)
– 4 –
where
β0 =
(11
3CA −
4
3TFnf
), β1 =
(34
3C2A −
20
3CATFnf − 4CFTFnf
)(2.10)
with CA = N , CF = (N2 − 1)/2N , TF = 1/2 and nf is the number of active quark
flavors. Since, the spin-2 resonance couples to the SM particles through energy momentum
tensor (eqn.(2.1)) which is conserved, the coupling constant κ is protected from any UV
renormalization. Hence, there will be no additional UV renormalization required other than
the strong coupling constant renormalization. Using the eqn.(2.9), we now can express |M〉(eqn.(2.8)) in powers of renormalized as with UV finite matrix elements |M(i)〉
|M〉 = (as)12
(|M(0)〉+ as|M(1)〉+ a2s|M(2)〉+O(a3s)
)(2.11)
where
|M(0)〉 =
(1
µεR
) 12
|M(0)〉 ,
|M(1)〉 =
(1
µεR
) 32 [|M(1)〉+ µεR
r12|M(0)〉
],
|M(2)〉 =
(1
µεR
) 52[|M(2)〉+ µεR
3r12|M(1)〉+ µ2εR
(r22− r21
8
)|M(0)〉
](2.12)
with
r1 =2β0ε, r2 =
(4β20ε2
+β1ε
). (2.13)
2.4 Infrared factorization
Beyond leading order, the UV renormalized matrix elements |M(i)〉, i > 0 contain di-
vergences arising from the infrared sector of massless QCD. They result from soft gluons
and collinear massless partons present in the loops. They will cancel against similar di-
vergences coming from real emission contributions in the infrared safe observables order
by order in as, thanks to KLN theorem [36, 37]. The infrared divergence structure and
their factorization property in QCD amplitudes have been well studied for long time. In
[30], Catani predicted the infrared divergences of multi-parton QCD amplitudes precisely
in dimensional regularization up to two loops excluding two loop single pole in ε. In [31],
Sterman and Tejeda-Yeomans provided a systematic way of understanding the structure of
infrared divergences using factorization properties of the scattering amplitudes along with
infrared evolution equations. They demonstrated the connection of single pole in ε to a
soft anomalous dimension matrix, later computed in [38, 39]. The structure of single pole
term for the electromagnetic and Higgs form factors was first shown in [40, 41]. Using soft
collinear effective field theory, Becher and Neubert [42] derived the exact formula for the
infra-red divergences of scattering amplitudes with an arbitrary number of loops and legs
in massless QCD including single pole in dimensional regularization. Using Wilson lines
– 5 –
for hard partons and soft and eikonal jet functions in dimensional regularization, Gardi
and Magnea also arrived at a similar all order result [43].
According to Catani’s prediction, the renormalized amplitudes |M(i)〉 for the process
(eqn.(2.3)) can be expressed in terms of the universal subtraction operators I(i)g (ε) as fol-
lows1
|M(1)〉 = 2 I(1)g (ε) |M(0)〉+ |M(1)fin〉
|M(2)〉 = 2 I(1)g (ε) |M(1)〉+ 4 I(2)g (ε) |M(0)〉+ |M(2)fin〉 (2.14)
where,
I(1)g (ε) =1
2
e−ε2γE
Γ(1 + ε2)Vsingg (ε)
[(− s
µ2R
) ε2
+(− t
µ2R
) ε2
+(− u
µ2R
) ε2
]
I(2)g (ε) = − 1
2I(1)g (ε)
[I(1)g (ε)− 2β0
ε
]+
eε2γE Γ(1 + ε)
Γ(1 + ε2)
[− β0
ε+K
]I(1)g (2ε)
+ H(2)g (ε) (2.15)
and
Vsingg (ε) = CA4
ε2− β0
ε, K =
(67
18− π2
6
)CA −
10
9TFnf (2.16)
H(2)g (ε) =
3
2ε
{C2A
(− 5
12− 11
24ζ2 −
1
2ζ3
)+ CAnf
(29
27+
1
12ζ2
)− 1
2CFnf −
5
27n2f
}(2.17)
3 Calculation of two-loop amplitude
We now describe the computation of 〈M(0)|M(1)〉 & 〈M(0)|M(2)〉 matrix elements where
all the Lorentz and color indices of external particles are summed over. The computation
involves large number of Feynman diagrams. We need to perform various algebraic sim-
plifications with Dirac, Lorentz and color indices before the loop integrals are evaluated.
Due to tensorial coupling of spin-2 resonance with the SM fields, the loops contain higher
rank tensor integrals as compared to the ones normally encountered in the SM processes.
We have systematically automated this computation using various symbolic manipulation
programs developed in house and few publicly available packages that use FORM [44] and
Mathematica. In the following, we describe the method in detail.
3.1 Feynman diagrams and simplification
We use QGRAF [45] to generate the Feynman diagrams. We find that there are 4 diagrams
at tree level, 108 at one loop and 2362 at two loops, leaving out tadpole and self energy
corrections to the external legs. The output of the QGRAF is then converted to the format
that is suitable for further symbolic manipulation using FORM and Mathematica. A set of
1The numerical coefficients 2 and 4 with I(i) come due to the different definition of as between ours and Catani.
– 6 –
FORM routines is used to perform simplification of the squared matrix elements involving
gluon and spin-2 resonance polarization and color sums. We have used Feynman gauge
throughout and for the external on-shell gluon legs, physical polarizations are summed
using ∑s
εµ(pi, s)εν∗(pi, s) = −gµν +
pµi qνi + qµi p
νi
p.q(3.1)
where, pi is the ith-gluon momentum and qi is the corresponding reference momentum
which is an arbitrary light-like 4-vector. We choose q1 = p2, q2 = p1 and q3 = p1 for
simplicity. The spin-2 polarization sum in d dimensions is given by [11]
Bµν;ρσ(q) =
(gµρ − qµqρ
q.q
)(gνσ − qνqσ
q.q
)+
(gµσ − qµqσ
q.q
)(gνρ − qνqρ
q.q
)− 2
d− 1
(gµν − qµqν
q.q
)(gρσ − qρqσ
q.q
)(3.2)
3.2 Reduction of tensor integrals
Beyond leading order, the resulting expressions involve tensorial one and two loop integrals
which need to be reduced to a set of scalar integrals using a convenient tensorial reduction
procedure. Tensorial reduction is quite straightforward at one loop level but not so at two
loop level and beyond. In addition, finding a minimal set of integrals after the tensorial
reduction is important to achieve the task with large number of Feynman integrals. A
systematic approach to deal with higher rank tensor integrals and large number of scalar
integrals is to use Integration by parts (IBP) [46] and Lorentz invariant (LI) [47] identities.
The IBP identities follow from the fact that in the dimensional regularization, the
integral of the total derivative with respect to any loop momenta vanishes, that is∫ddk1(2π)d
· · ·∫
ddkL(2π)d
∂
∂ki·(vj
1∏lD
nll
)= 0 (3.3)
where nl is an element of ~n = (n1, · · ·, nN ) with nl ∈ Z, L is the number of loops and Dlsare propagators which depend on the loop and external momenta and also masses. The
four vector vµj can be both loop and external momenta. Performing the differentiation on
the left hand side and expressing the scalar products of ki and pj linearly in terms of Dl’s,one obtains the IBP identities given by∑
i
aiJ(bi,1 + n1, ..., bi,N + nN ) = 0 (3.4)
where
J(~m) = J(m1, · · ·,mN ) =
∫ddk1(2π)d
· · · ddkL
(2π)d1∏lD
mll
(3.5)
with bi,j ∈ {−1, 0, 1} and ai are polynomial in nj . The LI identities follow from the fact that
the loop integrals are invariant under Lorentz transformations of the external momenta,
that is
pµi pνj
(∑k
pk[ν∂
∂pµ]k
)J(~n) = 0. (3.6)
– 7 –
While these identities are useful to express the tensorial integrals in terms of a set of
master integrals, in practice, the computation becomes tedious due to the appearance of
large variety of Feynman integrals involving different set of propagators each requiring a
set of IBP and LI identities independently. We have reduced such varieties to a few by
shifting the loop momenta suitably using an in-house algorithm which uses FORM. For
one-loop diagrams, we can express each Feynman integral to contain terms from one of the
following three sets:
{D, D1, D12, D123} , {D, D2, D23, D123} , {D, D3, D31, D123} (3.7)
where,
D = k21, Di = (k1 − pi)2, Dij = (k1 − pi − pj)2, Dijk = (k1 − pi − pj − pk)2 (3.8)
In each set in eqn.(3.7), D’s are linearly independent and form a complete basis in the
sense that any Lorentz invariant k1 · pi can be expressed in terms of D’s. At two loops,
there are nine independent Lorentz invariants involving loop momenta k1 and k2, namely
{(kα · kβ), (kα · pi)}, α, β = 1, 2; i = 1, ..., 3. After appropriate shifting of loop momenta,
we can express each two loop Feynman integral to contain terms belonging to one of the
following six sets:
{D0, D1, D2, D1;1, D2;1, D1;12, D2;12, D1;123, D2;123}
{D0, D1, D2, D1;2, D2;2, D1;23, D2;23, D1;123, D2;123}
{D0, D1, D2, D1;3, D2;3, D1;31, D2;31, D1;123, D2;123}
{D0, D1, D2, D1;1, D2;1, D0;3, D1;12, D2;12, D1;123}
{D0, D1, D2, D1;2, D2;2, D0;1, D1;23, D2;23, D1;123}
{D0, D1, D2, D1;3, D2;3, D0;2, D1;31, D2;31, D1;123} (3.9)
where,
D0 = (k1 − k2)2, Dα = k2α, Dα;i = (kα − pi)2, Dα;ij = (kα − pi − pj)2,
D0;i = (k1 − k2 − pi)2, Dα;ijk = (kα − pi − pj − pk)2 (3.10)
Given the fewer number of sets (eqns.(3.7) & (3.9)), it is easier to use IBP and LI
identities using Laporta algorithm [48]. These identities can be generated using publicly
available packages such as AIR [49], FIRE [50], REDUZE [51, 52], LiteRed [53, 54] etc. For
our computation, we use a Mathematica based package LiteRedV1.51 along with MintV1.1
[55]. This package has the option to exploit symmetry relations within each set and also
among different sets.
– 8 –
Figure 1. Planar topologies of master integrals
3.3 Master integrals
Using these IBP and LI identities, we reduce all the integrals that appear in our computa-
tion to a minimal set of master integrals. For one loop, we get two topologically different
master integrals namely box and bubble, see Fig.(1) and we find that the master integrals
with three propagators are absent. For two loops, we encounter 16 planar and 5 non-planar
topologies of master integrals. These master integrals can be related to those that were
– 9 –
Figure 2. Non-Planar topologies of master integrals
computed by Gehrmann and Remiddi in their seminal papers [34, 35]. In particular, our
set of master integrals does not contain integrals with irreducible numerator, instead we
have higher power of propagators. We use IBP and LI identities to express our set of mas-
ter integrals to those of [34, 35]. All the master integrals are drawn in Fig.(1) and Fig.(2)
up to different permutations of the external momenta p1, p2 and p3. We also observe that
some topologies like iXBox1 given in Fig.(2) are absent in our final result and find some
new topologies namely Glass3S and Kite1 given in Fig.(1) which are absent in the [34, 35]
and those are simply a product of two one loop topologies.
Substituting the master integrals computed by Gehrmann and Remiddi [34, 35] in
terms of HPLs and 2dHPLs, we obtain the unrenormalized matrix elements 〈M(0)|M(1)〉and 〈M(0)|M(2)〉. We use shuffle algebra to express product of lower weight HPLs as a
sum of higher weight HPLs. In the next section we present our results.
4 Results
The UV renormalized matrix elements 〈M(0)|M(1)〉 and 〈M(0)|M(2)〉 are computed using
the unrenormalized counter parts through
〈M(0)|M(1)〉 =
(1
µεR
)2 [〈M(0)|M(1)〉+ µεR
r12〈M(0)|M(0)〉
],
〈M(0)|M(2)〉 =
(1
µεR
)3 [〈M(0)|M(2)〉+ µεR
3r12〈M(0)|M(1)〉
+ µ2εR
(r22− r21
8
)〈M(0)|M(0)〉
]. (4.1)
Using eqn.(2.14), we can also express the renormalized matrix elements in terms of I(i)g (ε),
given by
〈M(0)|M(1)〉 = 2 I(1)g (ε) 〈M(0)|M(0)〉+ 〈M(0)|M(1)fin〉 ,
〈M(0)|M(2)〉 = 2 I(1)g (ε) 〈M(0)|M(1)〉+ 4 I(2)g (ε) 〈M(0)|M(0)〉+ 〈M(0)|M(2)fin〉 .(4.2)
– 10 –
Expanding the right hand side of equations (4.1 & 4.2) in powers of ε and comparing their
coefficients of O(ε0), we obtain 〈M(0)|M(1)fin〉 and 〈M(0)|M(2)fin〉.We find that all the poles in ε resulting from the soft and collinear partons in eqn.(4.1)
are in agreement with those of eqn.(4.2). This serves as an important check on our result.
In addition, it establishes the universal structure of infrared poles in QCD amplitudes
involving tensorial operator insertion. We also observe that the contributions resulting
from the gauge fixing term in eqn.(2.1) cancel exactly with those of ghosts confirming the
gauge independence of our result. As we anticipated, the eqn.(4.1) does not require any
over all operator renormalization constant due to the conservation of energy momentum
tensor and it can be made UV finite through strong coupling constant renormalization
(eqn.(2.9)) alone. Below we present our final results
〈M(0)|M(0)〉 = Fh A(0) ,
〈M(0)|M(1)fin〉 = Fh
{− β0
2A(0) ln
(−Q
2
µ2
)+(A(1)
1 ζ2 +A(1)2
)},
〈M(0)|M(2)fin〉 = Fh
{3β208A(0) ln2
(−Q
2
µ2
)
〈M(0)|M(2)finFh〉+(−3 C2
A ζ3 A(0) +A(2)1 ζ2 +A(2)
2
)ln
(−Q
2
µ2
)
〈M(0)|M(2)finFh〉+(A(2)
3 ζ22 +A(2)4 ζ3 +A(2)
5 ζ2 +A(2)6
)}(4.3)
where,
Fh = 16π2κ2N(N2 − 1
),
A(0) =4
stu
(s4 + 2s3(t+ u) + 3s2
(t2 + u2
)+ 2s
(t3 + u3
)+(t2 + tu+ u2
)2),
A(1)α = A(1)
α;CACA +A(1)
α;nfnf ,
A(2)α = A(2)
α;C2AC2A +A(2)
α;CAnf CAnf +A(2)α;CFnf CFnf +A(2)
α;n2fn2f . (4.4)
The coefficients A(i)α;C are given in the appendix except A(2)
6;CAnf, A(2)
6;CFnf& A(2)
6;n2f
which
can be found in the files A6Canf, A6Cfnf and A6nf2 respectively attached with this arXiv
submission.
5 Conclusion
The computation of one and two loop QCD results for the process h→ g+g+g is presented.
We use dimensional regularization to regulate both UV and IR divergences. Our result is
– 11 –
very general in the sense that it can be used for any scattering process involving production
of a massive spin-2 particle that has a universal coupling with the SM fields. We can use
it to study the production of a jet with missing energy due to KK graviton escaping the
detector or a process with resonant massive spin-2 particle in association with a jet. Since
the spin-2 field couples with the SM ones through rank-2 tensor, we not only encounter large
number of Feynman diagrams but also the formidable challenge of reducing one and two
loop Feynman integrals with high powers of loop momenta to scalar ones. The IBP and LI
identities reduce all such integrals to only few master integrals that were already computed
by Gehrmann and Remiddi. This computation is the first of the kind involving four point
function at two loop level in QCD with tensorial insertion and one massive external state.
We find that no overall UV renormalization is required due to the conservation of energy
momentum tensor. We also find that our results exhibit the right IR structure confirming
the factorization property of QCD amplitude even with tensorial insertion.
Acknowledgement
MM, TA and NR thank for the hospitality provided by the Institute of Mathematical
Sciences (IMSc) where the work was carried out. We thank the staff of IMSc computer
center for their help. We sincerely thank T. Gehrmann for providing us the master integrals
required for our computation. We thank R. N. Lee for his help with LiteRed, and A.V.
Smirnov and V.A. Smirnov for their suggestions with FIRE. Finally, we would like to thank
K. Hasegawa, M. K. Mandal and L. Tancredi for discussions and their valuable suggestions.
NR, TA and MM also like to thank their parents and siblings for their wonderful love and
continuous support.
– 12 –
A Harmonic polylogarithms
In this section, we briefly describe the definition and properties of HPL and 2dHPL. HPL is
represented by H(~mw; y) with a w-dimensional vector ~mw of parameters and its argument
y. w is called the weight of the HPL. The elements of ~mw belong to {1, 0,−1} through
which the following rational functions are represented
f(1; y) ≡ 1
1− y, f(0; y) ≡ 1
y, f(−1; y) ≡ 1
1 + y. (A.1)
The weight 1 (w = 1) HPLs are defined by
H(1, y) ≡ − ln(1− y), H(0, y) ≡ ln y, H(−1, y) ≡ ln(1 + y) . (A.2)
For w > 1, H(m, ~mw; y) is defined by
H(m, ~mw; y) ≡∫ y
0dx f(m,x) H(~mw;x), m ∈ 0,±1 . (A.3)
The 2dHPLs are defined in the same way as eqn.(A.3) with the new elements {2, 3} in ~mw
representing a new class of rational functions
f(2; y) ≡ f(1− z; y) ≡ 1
1− y − z, f(3; y) ≡ f(z; y) ≡ 1
y + z(A.4)
and correspondingly with the weight 1 (w = 1) 2dHPLs
H(2, y) ≡ − ln(
1− y
1− z
), H(3, y) ≡ ln
(y + z
z
). (A.5)
Properties
Shuffle algebra : A product of two HPL with weights w1 and w2 of the same argument y
is a combination of HPLs with weight (w1 + w2) and argument y, such that all possible
permutations of the elements of ~mw1 and ~mw2 are considered preserving the relative orders
of the elements of ~mw1 and ~mw2 ,
H(~mw1 ; y)H(~mw2 ; y) =∑
~mw = ~mw1] ~mw2
H(~mw; y). (A.6)
Integration-by-parts identities : The ordering of the elements of ~mw in an HPL with weight
w and argument y can be reversed using integration-by-parts and in the process, some
products of two HPLs are generated in the following way
H(~mw; y) ≡ H(m1,m2, ...,mw; y) = H(m1, y)H(m2, ...,mw; y)
− H(m2,m1, y)H(m3, ...,mw; y)
+ ...+ (−1)w+1H(mw, ...,m2,m1; y) . (A.7)
– 13 –
B One-loop coefficients
A(1)1;CA
= −4
stu
(s4
+ 2s3(t + u) + 3s
2(t2
+ u2)
+ 2s(t3
+ u3)
+ t4
+ u4)
A(1)1;nf
= −2
s
(t2
+ u2)
A(1)2;CA
=
{− 6(t + u)
4(11s
8+ 22(3t + u)s
7+(187t
2+ 64ut + 33 u
2)s6
+(330t
3+ 60ut
2+ 78u
2t + 22u
3)s5
+(396 t
4+ 14ut
3
+ 51u2t2
+ 36u3t+ 11u
4)s4
+ 2t(165t
4+ 7u t
3+ 6u
2t2
+ 7u3t+ 10u
4)s3
+ t2(187t
4+ 60ut
3+ 51u
2t2
+ 14u3t+ 24u
4)s2
+ 2t3(33t
4+ 32ut
3+ 39u
2t2
+ 18u3t+ 10u
4)s+ 11t
4(t2
+ut+u2)2)
H(0, y)(s+u)4− 36 (s+ t)
4(t+u)
4(s4
+ 2(t+u)s3
+ 3(t2
+ u2)s2
+ 2(t3
+ u3)s + t
4+ u
4)H(0, y)H(0, z)(s + u)
4+ 6(s + t)
4((
11t4
+ 20ut3
+ 24u2t2
+ 20u3t+ 11u
4)s4
+ 2(11 t
5+ 18ut
4+ 7u
2t3
+ 7u3t2
+ 18u4t+ 11u
5)s3
+ 3(t+u)2(11t
4+ 4ut
3 − 2u2t2
+ 4u3t+ 11u
4)s2
+ 2(t+u)3(11 t
4
−ut3−u3t+ 11u
4)s+ 11(t+u)
4(t2
+ut+u2)2)
H(1, z)(s+u)4
+ 36(s+ t)4(t+u)
4(s4
+ 2ts3
+ 3t2s2
+ 2t3s+
(t2
+ut
+ u2)2)
H(0, y)H(1, z)(s+ u)4
+ 6(s+ t)4((
11t4
+ 20ut3
+ 24u2t2
+ 20u3t+ 11u
4)s4
+ 2(11 t
5+ 18ut
4+ 7u
2t3
+ 7u3t2
+18u4t+11u
5)s3
+3(t+u)2(11t
4+4ut
3−2u2t2
+4u3t+11u
4)s2
+2(t+u)3(11 t
4−ut3−u3t+11u
4)s+11(t+u)
4(t2
+ ut + u2)2)
H(2, y)(s + u)4
+ 36(s + t)4(t + u)
4(s4
+ 2us3
+ 3u2s2
+ 2u3s +
(t2
+ ut + u2)2)
H(0, z)H(2, y)(s + u)4
− 36(s + t)4(t + u)
4(2s
4+ 2(t + u)s
3+ 3
(t2
+ u2)s2
+ 2(t3
+ u3)s + 2
(t2
+ ut + u2)2)
H(1, z)H(3, y)(s + u)4
− 36(s + t)4
(t + u)4(s4
+ 2ts3
+ 3t2s2
+ 2t3s +
(t2
+ u t + u2)2)
H(0, 1, z)(s + u)4
+ 36(s + t)4(t + u)
4(s4
+ 2t s3
+ 3t2s2
+ 2t3s +
(t2
+ ut + u2)2)
H(0, 2, y)(s + u)4 − 36 (s + t)
4(t + u)
4(2s
4+ 2(2t + u)s
3+ 3
(2t
2+ u
2)s2
+ 2(2t
3
+ u3)s+ 2t
4+ 2u
4+ 2tu
3+ 3t
2u2
+ 2t3u)H(1, 0, y)(s+ u)
4 − 36(s+ t)4(t+ u)
4(s4
+ 2(t+ u)s3
+ 3(t2
+ u2)s2
+ 2(t3
+ u3)s + t
4+ u
4)H(1, 0, z) (s + u)
4+ 36(s + t)
4(t + u)
4(s4
+ 2ts3
+ 3t2s2
+ 2t3s +
(t2
+ u t + u2)2)
H(2, 0, y)(s + u)4
− 36(s + t)4(t + u)
4(2s
4+ 2 (t + u)s
3+ 3
(t2
+ u2)s2
+ 2(t3
+ u3)s + 2
(t2
+ u t + u2)2)
H(3, 2, y)(s + u)4
=− 2(s+ t)(t+ u)(203(t+ u)
3s10
+ 2(506t
4+ 1988ut
3+ 2973u
2t2
+ 1988u3t+ 506u
4)s9
+ 3(807t
5+ 3709ut
4+ 7123u
2t3
+ 7123u3t2
+ 3709u4t + 807 u
5)s8
+ 3(1208t
6+ 6186ut
5+ 13887u
2t4
+ 17836u3t3
+ 13887 u4t2
+ 6186u5t + 1208u
6)s7
+(3624t
7+ 21596ut
6+ 54318u
2t5
+ 80567u3t4
+ 80567u4t3
+ 54318u5t2
+ 21596u6t + 3624u
7)s6
+ 3(807t
8+ 6186ut
7
+ 18106u2t6
+ 29776u3t5
+ 34116u4t4
+ 29776u5t3
+ 18106u6t2
+ 6186u7t+ 807u
8)s5
+(1012 t
9+ 11127ut
8+ 41661u
2t7
+80567u3t6
+102348u4t5
+102348u5t4
+80567u6t3
+41661u7t2
+11127u8t+1012u
9)s4
+(203 t
10+3976ut
9+21369u
2t8
+53508u3t7
+80567u4t6
+89328u5t5
+80567u6t4
+53508u7t3
+21369u8t2
+3976u9t+203u
10)s3
+3tu(203t
9+1982ut
8
+ 7123u2t7
+ 13887u3t6
+ 18106u4t5
+ 18106u5t4
+ 13887u6t3
+ 7123u7t2
+ 1982u8t + 203u
9)s2
+ t2u2(t + u)
2(609t
6
+ 2758ut5
+ 5002u2t4
+ 5796u3t3
+ 5002 u4t2
+ 2758u5t + 609u
6)s + t
3u3(t + u)
3(203t
4+ 403u t
3+ 603u
2t2
+ 403u3t
+ 203u4))
(s+ u)− 6(s+ t)4(t+ u)
4(11s
8+ 22(t+ 3u)s
7+(33t
2+ 64ut+ 187u
2)s6
+(22 t
3+ 78ut
2+ 60u
2t+ 330u
3)s5
+(11t
4+36ut
3+51u
2t2
+14 u3t+396u
4)s4
+2u(10t
4+7ut
3+6u
2t2
+7u3t+165 u
4)s3
+u2(24t
4+14ut
3+51u
2t2
+60u3t
+187u4)s2
+2u3(10t
4+18ut
3+39u
2t2
+32u3t+33u
4)s+11u
4(t2
+ut+u2)2)
H(0, z)
}/(9st(s + t)
4u(s + u)
4(t + u)
4)
A(1)2;nf
=
{− 18u(s + u)
4(t + u)
4(s2 − ts + t
2+ u
2)H(1, 0, y)(s + t)
5+ 6 (t + u)
4(2s
8+ 4(t + 3u)s
7+ 2
(3t
2+ 5ut + 17u
2)s6
+(4t
3+ 15ut
2+ 6u
2t + 60u
3)s5
+ 2(t4
+ 12u2t2 − 2 u
3t + 36u
4)s4
+ 2u(t4 − 2ut
3+ 15u
2t2 − 2u
3t + 30 u
4)s3
+ 2u2(3t
4 − 2ut3
+ 12u2t2
+ 3u3t+ 17u
4)s2
+(12u
7+ 10tu
6+ 15t
2u5
+ 2t4u3)s+ 2u
4(t2
+ u t+ u2)2)
H(0, z)(s+ t)4
− 18tu(s + u)4(t + u)
4(t2
+ u2)H(0, y)H(0, z)(s + t)
4 − 6(s + u)4(2(t4
+ u t3
+ 3u2t2
+ u3t + u
4)s4
+ 4(t5 − u2
t3
− u3t2
+ u5)s3
+ 3(t+ u)2(2t
4+ ut
3+ 4u
2t2
+ u3t+ 2u
4)s2
+ 2(t+ u)3(2t
4 − ut3 − u3t+ 2u
4)s+ 2(t+ u)
4(t2
+ u t
+ u2)2)
H(1, z)(s + t)4
+ 18su(s + u)4(t + u)
4(s2
+ u2)H(0, y)H(1, z)(s + t)
4 − 6(s + u)4(2(t4
+ u t3
+ 3u2t2
+ u3t
+u4)s4
+ 4(t5 −u2
t3 −u3
t2
+u5)s3
+ 3(t+u)2(2t
4+ut
3+ 4u
2t2
+u3t+ 2u
4)s2
+ 2(t+u)3(2t
4 −ut3 −u3t+ 2u
4)s
+ 2(t+u)4(t2
+u t+u2)2)
H(2, y)(s+ t)4
+ 18st(s2
+ t2)(s+u)
4(t+u)
4H(0, z)H(2, y)(s+ t)
4− 18s(s+u)4(t+u)
5(s2
+ t2
+ u2 − t u
)H(1, z)H(3, y)(s + t)
4 − 18su(s + u)4(t + u)
4(s2
+ u2)H(0, 1, z)(s + t)
4+ 18su(s + u)
4(t + u)
4(s2
+u2)H(0, 2, y) (s+ t)
4− 18tu(s+u)4(t+u)
4(t2
+u2)H(1, 0, z)(s+ t)
4+ 18su (s+u)
4(t+u)
4(s2
+u2)H(2, 0, y)(s+ t)
4
– 14 –
=− 18s(s+ u)4(t+ u)
5(s2
+ t2
+ u2 − tu
)H(3, 2, y)(s+ t)
4+ 2(s+ u)(t+ u)
(35(t+ u)
3s10
+ 2(86t
4+ 335ut
3+ 507u
2t2
+ 335u3t + 86u
4)s9
+ 3(135t
5+ 607ut
4+ 1177u
2t3
+ 1177u3t2
+ 607u4t + 135u
5)s8
+ 3(200t
6+ 990ut
5+ 2211u
2t4
+ 2860u3t3
+ 2211u4t2
+ 990u5t + 200u
6)s7
+(600t
7+ 3428ut
6+ 8436u
2t5
+ 12593u3t4
+ 12593u4t3
+ 8436u5t2
+ 3428u6t+ 600u
7)s6
+ 3(135 t
8+ 990ut
7+ 2812u
2t6
+ 4612u3t5
+ 5328u4t4
+ 4612u5t3
+ 2812u6t2
+ 990u7t+ 135u
8)s5
= +(172t
9+ 1821ut
8+ 6633u
2t7
+ 12593 u3t6
+ 15984u4t5
+ 15984u5t4
+ 12593u6t3
+ 6633u7t2
+ 1821u8t + 172u
9)s4
+(35t
10+ 670ut
9+ 3531u
2t8
+ 8580u3t7
+ 12593u4t6
+ 13836u5t5
+ 12593u6t4
+ 8580u7t3
+ 3531u8t2
+ 670 u9t
+35u10)s3
+3tu(35t
9+338ut
8+1177u
2t7
+2211 u3t6
+2812u4t5
+2812u5t4
+2211u6t3
+1177u7t2
+338u8t+35 u
9)s2
+ t2u2(t+ u)
2(105t
6+ 460ut
5+ 796u
2t4
+ 918u3t3
+ 796u4t2
+ 460u5t+ 105u
6)s+ t
3u3(t+ u)
3(35t
4+ 67u t
3+ 99u
2t2
+ 67u3t + 35u
4))
(s + t) + 6(s + u)4(t + u)
4(2 s
8+ 4(3t + u)s
7+ 2
(17t
2+ 5ut + 3u
2)s6
+(60t
3+ 6u t
2+ 15u
2t
+ 4u3)s5
+ 2(36t
4 − 2ut3
+ 12u2t2
+ u4)s4
+ 2t(30t
4 − 2ut3
+ 15u2t2 − 2u
3t + u
4)s3
+ 2t2(17t
4+ 3ut
3+ 12u
2t2
− 2u3t + 3u
4)s2
+(12t
7+ 10u t
6+ 15u
2t5
+ 2u4t3)s + 2t
4(t2
+ ut + u2)2)
H(0, y)
}/(9st(s + t)
4u(s + u)
4(t + u)
4)
C Two-loop coefficients
A(2)
1;C2A
=11
stu
(s4
+ 2s3(t + u) + 3s
2(t2
+ u2)
+ 2s(t3
+ u3)
+ t4 − 2t
3u− 3t
2u2 − 2tu
3+ u
4)
A(2)1;CAnf
= −1
stu
(2s
4+ 4s
3(t + u) + 6s
2(t2
+ u2)
+ 4s(t3
+ u3)
+ 2t4 − 15t
3u− 6t
2u2 − 15tu
3+ 2u
4)
A(2)1;CF nf
= 0
A(2)
1;n2f
= −2
s
(t2
+ u2)
A(2)
2;C2A
=
{33(t+u)
4(11s
8+ 22(3t+u)s
7+(187t
2+ 64ut+ 33 u
2)s6
+(330t
3+ 60ut
2+ 78u
2t+ 22u
3)s5
+(396 t
4+ 14ut
3+ 51u
2t2
=+36u3t+11u
4)s4
+2t(165t
4+7u t
3+6u
2t2
+7u3t+10u
4)s3
+ t2(187t
4+60ut
3+51u
2t2
+14u3t+24u
4)s2
+2t3(33t
4+32ut
3
+ 39u2t2
+ 18u3t+ 10u
4)s+ 11t
4(t2
+ ut+ u2)2)
H(0, y) (s+ u)4
+ 198(s+ t)4(t+ u)
4(s4
+ 2(t+ u)s3
+ 3(t2
+ u2)s2
+ 2(t3
+u3)s+ t
4+u
4)H(0, y)H(0, z)(s+u)
4−33(s+ t)4((
11t4
+ 20ut3
+ 24u2t2
+ 20u3t+ 11u
4)s4
+ 2(11 t
5+ 18ut
4+ 7u
2t3
+ 7u3t2
+ 18u4t+ 11u
5)s3
+ 3(t+u)2(11t
4+ 4ut
3 − 2u2t2
+ 4u3t+ 11u
4)s2
+ 2(t+u)3(11 t
4 −ut3 −u3t+ 11u
4)s+ 11(t+u)
4(t2
+ut
+u2)2)
H(1, z)(s+u)4−198(s+ t)
4(t+u)
4(s4
+2ts3
+3t2s2
+2t3s+
(t2
+ut+u2)2)
H(0, y)H(1, z)(s+u)4−33(s+ t)
4((
11t4
+ 20ut3
+ 24u2t2
+ 20u3t+ 11u
4)s4
+ 2(11 t
5+ 18ut
4+ 7u
2t3
+ 7u3t2
+ 18u4t+ 11u
5)s3
+ 3(t+u)2(11t
4+ 4ut
3− 2u2t2
+ 4u3t
+ 11u4)s2
+ 2(t+ u)3(11 t
4 − ut3 − u3t+ 11u
4)s+ 11(t+ u)
4(t2
+ ut+ u2)2)
H(2, y)(s+ u)4 − 198(s+ t)
4(t+ u)
4(s4
+ 2us3
+ 3u2s2
+ 2u3s+
(t2
+ ut+ u2)2)
H(0, z)H(2, y)(s+ u)4
+ 198(s+ t)4
(t+ u)4(2s
4+ 2(t+ u)s
3+ 3(t2
+ u2)s2
+ 2(t3
+ u3)s
+ 2(t2
+ ut+ u2)2)
H(1, z)H(3, y) (s+ u)4
+ 198(s+ t)4(t+ u)
4(s4
+ 2ts3
+ 3t2s2
+ 2t3s+
(t2
+ u t+ u2)2)
H(0, 1, z)(s+ u)4
=− 198(s + t)4(t + u)
4(s4
+ 2t s3
+ 3t2s2
+ 2t3s +
(t2
+ ut + u2)2)
H(0, 2, y)(s + u)4
+ 198 (s + t)4(t + u)
4(2s
4+ 2(2t + u)s
3
+ 3(2t
2+ u
2)s2
+ 2(2t
3+ u
3)s + 2t
4+ 2u
4+ 2tu
3+ 3t
2u2
+ 2t3u)H(1, 0, y)(s + u)
4+ 198(s + t)
4(t + u)
4(s4
+ 2(t + u)s3
+ 3(t2
+ u2)s2
+ 2(t3
+ u3)s + t
4+ u
4)H(1, 0, z) (s + u)
4 − 198(s + t)4(t + u)
4(s4
+ 2ts3
+ 3t2s2
+ 2t3s +
(t2
+ u t
+u2)2)
H(2, 0, y)(s+u)4
+198(s+ t)4(t+u)
4(2s
4+2 (t+u)s
3+3(t2
+u2)s2
+2(t3
+u3)s+2
(t2
+u t+u2)2)
H(3, 2, y)(s+u)4
– 15 –
= + (s+ t)(t+ u)(1939(t+ u)
3s10
+(9662t
4+ 37856ut
3+ 56586u
2t2
+ 37856u3t+ 9662u
4)s9
+ 3(7701t
5+ 35213ut
4+ 67475u
2t3
+ 67475u3t2
+ 35213u4t+ 7701u
5)s8
+ 3(11524t
6+ 58638ut
5+ 131001u
2t4
+ 167972 u3t3
+ 131001u4t2
+ 58638u5t+ 11524u
6)s7
+(34572 t
7+ 204628ut
6+ 511062u
2t5
+ 754525u3t4
+ 754525u4t3
+ 511062u5t2
+ 204628u6t + 34572u
7)s6
+ 3(7701t
8
+ 58638ut7
+ 170354 u2t6
+ 278144u3t5
+ 317652u4t4
+ 278144u5t3
+ 170354u6t2
+ 58638 u7t+ 7701u
8)s5
+(9662t
9+ 105639ut
8
+393003u2t7
+754525 u3t6
+952956u4t5
+952956u5t4
+754525u6t3
+393003u7t2
+105639 u8t+9662u
9)s4
+(1939t
10+37856ut
9
+ 202425u2t8
+ 503916u3t7
+ 754525u4t6
+ 834432u5t5
+ 754525u6t4
+ 503916u7t3
+ 202425u8t2
+ 37856u9t + 1939u
10)s3
+3tu(1939 t
9+18862ut
8+67475u
2t7
+131001u3t6
+170354u4t5
+170354u5t4
+131001u6t3
+67475u7t2
+18862u8t+1939u
9)s2
+ t2u2
(t+u)2(5817t
6+ 26222ut
5+ 47378u
2t4
+ 54936u3t3
+ 47378u4t2
+ 26222u5t+ 5817u
6)s+ t
3u3(t+u)
3(1939t
4+ 3845u t
3
+5751u2t2
+3845u3t+1939u
4))
(s+u)+33(s+t)4(t+u)
4(11s
8+22(t+3u)s
7+(33t
2+64ut+187u
2)s6
+(22 t
3+78ut
2+60u
2t
+330u3)s5
+(11t
4+36ut
3+51u
2t2
+14 u3t+396u
4)s4
+2u(10t
4+7ut
3+6u
2t2
+7u3t+165 u
4)s3
+u2(24t
4+14ut
3+51u
2t2
+60u3t+187u
4)s2
+2u3(10t
4+18ut
3+39u
2t2
+32u3t+33u
4)s+11u
4(t2
+ut+u2)2)
H(0, z)
}/(9st(s + t)
4u(s + u)
4(t + u)
4)
A(2)2;CAnf
= −{
3(t+u)4(44s
8+ 88(3t+u)s
7+ 2(374t
2+ 119ut+ 66 u
2)s6
+(1320t
3+ 186ut
2+ 321u
2t+ 88u
3)s5
+ 2(792t
4− 8ut3
= + 183u2t2
+ 36u3t+ 22u
4)s4
+ 2t(660 t
4 − 8ut3
+ 177u2t2 − 8u
3t+ 31u
4)s3
+ 2t2(374t
4+ 93u t
3+ 183u
2t2 − 8u
3t+ 57u
4)s2
+ t3(264t
4+ 238ut
3+ 321 u
2t2
+ 72u3t + 62u
4)s + 44t
4(t2
+ ut + u2)2)
H(0, y)(s + u)4
+ 9(s + t)4(t + u)
4(4s
4+ 8(t + u)s
3
+ 12(t2
+ u2)s2
+ 8(t3
+ u3)s + 4t
4+ 4u
4 − 11tu3 − 11 t
3u)H(0, y)H(0, z)(s + u)
4 − 3(s + t)4(2(22t
4+ 31u t
3+ 57u
2t2
+ 31u3t + 22u
4)s4
+ 8(11t
5+ 9ut
4 − 2u2t3 − 2 u
3t2
+ 9u4t + 11u
5)s3
+ 3(t + u)2(44t
4+ 19ut
3+ 40u
2t2
+ 19u3t + 44u
4)s2
+ 2(t+ u)3(44t
4 − 13ut3 − 13u
3t+ 44 u
4)s+ 44(t+ u)
4(t2
+ ut+ u2)2)
H(1, z)(s+ u)4 − 9 (s+ t)
4(t+ u)
4(4s
4+ (8t− 11u)s
3
+ 12t2s2
+(8t
3 − 11 u3)s + 4
(t2
+ ut + u2)2)
H(0, y)H(1, z)(s + u)4 − 3 (s + t)
4(2(22t
4+ 31ut
3+ 57u
2t2
+ 31u3t + 22u
4)s4
+ 8(11t
5+ 9ut
4 − 2u2t3 − 2u
3t2
+ 9u4t + 11u
5)s3
+ 3 (t + u)2(44t
4+ 19ut
3+ 40u
2t2
+ 19u3t + 44u
4)s2
+ 2 (t + u)3(44t
4
− 13ut3 − 13u
3t+ 44u
4)s+ 44(t+ u)
4(t2
+ ut+ u2)2)
H(2, y)(s+ u)4 − 9(s+ t)
4(t+ u)
4(4 s
4+ (8u− 11t)s
3+ 12u
2s2
+(8u
3
− 11t3)s + 4
(t2
+ u t + u2)2)
H(0, z)H(2, y)(s + u)4
+ 9(s + t)4(t + u)
4(8s
4 − 3 (t + u)s3
+ 12(t2
+ u2)s2 − 3
(t3
+ u3)s
+ 8(t2
+ u t + u2)2)
H(1, z)H(3, y)(s + u)4
+ 9(s + t)4(t + u)
4(4s
4+ (8 t− 11u)s
3+ 12t
2s2
+(8t
3 − 11u3)s + 4
(t2
+ u t
+ u2)2)
H(0, 1, z)(s+ u)4 − 9(s+ t)
4(t+ u)
4(4s
4+ (8t− 11 u)s
3+ 12t
2s2
+(8t
3 − 11u3)s+ 4
(t2
+ u t+ u2)2)
H(0, 2, y)(s+ u)4
+ 9(s+ t)4(t+ u)
4(8s
4+ (16t− 3 u)s
3+ 12
(2t
2+ u
2)s2
+(16t
3 − 3u3)s+ 8t
4+ 8 u
4 − 3tu3
+ 12t2u2 − 3t
3u)H(1, 0, y)(s+ u)
4
+ 9(s + t)4(t + u)
4(4s
4+ 8(t + u)s
3+ 12
(t2
+ u2)s2
+ 8(t3
+ u3)s + 4t
4+ 4u
4 − 11tu3 − 11t
3u)H(1, 0, z)(s + u)
4
− 9(s+ t)4(t+ u)
4(4s
4+ (8t− 11u)s
3+ 12t
2s2
+(8t
3 − 11u3)s+ 4
(t2
+ ut+ u2)2)
H(2, 0, y)(s+ u)4
+ 9(s+ t)4(t+ u)
4(8 s
4
−3(t+u)s3
+12(t2
+u2)s2−3
(t3
+u3)s+8
(t2
+ut+u2)2)
H(3, 2, y)(s+u)4
+(s+t)(t+u)(499 (t+u)
3s10
+2(1228t
4+4741ut
3
= + 7143u2t2
+ 4741u3t + 1228 u
4)s9
+ 3(1931t
5+ 8547ut
4+ 16389u
2t3
+ 16389u3t2
+ 8547 u4t + 1931u
5)s8
+ 3(2864t
6
+ 13918ut5
+ 30487u2t4
+ 39100 u3t3
+ 30487u4t2
+ 13918u5t + 2864u
6)s7
+(8592t
7+ 48196u t
6+ 115584u
2t5
+ 168841u3t4
+ 168841u4t3
+ 115584u5t2
+ 48196u6t + 8592u
7)s6
+ 3(1931t
8+ 13918ut
7+ 38528u
2t6
+ 61228u3t5
+ 69608u4t4
+ 61228u5t3
+ 38528u6t2
+ 13918u7t + 1931u
8)s5
+(2456t
9+ 25641ut
8+ 91461u
2t7
+ 168841u3t6
+ 208824u4t5
+ 208824u5t4
+ 168841u6t3
+ 91461u7t2
+ 25641u8t+ 2456u
9)s4
+(499t
10+ 9482ut
9+ 49167u
2t8
+ 117300u3t7
+ 168841u4t6
+ 183684u5t5
+ 168841u6t4
+ 117300u7t3
+ 49167u8t2
+ 9482u9t+ 499u
10)s3
+ 3tu(499t
9+ 4762ut
8+ 16389u
2t7
+ 30487 u3t6
+ 38528u4t5
+ 38528u5t4
+ 30487u6t3
+ 16389u7t2
+ 4762u8t + 499u
9)s2
+ t2u2(t + u)
2(1497t
6+ 6488ut
5+ 11168u
2t4
+ 12930u3t3
+ 11168u4t2
+ 6488u5t + 1497u
6)s + t
3u3(t + u)
3(499t
4+ 959ut
3+ 1419u
2t2
+ 959u3t + 499u
4))
(s + u)
+ 3 (s + t)4(t + u)
4(44s
8+ 88(t + 3u)s
7+ 2
(66t
2+ 119ut + 374 u
2)s6
+(88t
3+ 321ut
2+ 186u
2t + 1320u
3)s5
+ 2(22t
4
+ 36ut3
+ 183u2t2 − 8u
3t + 792u
4)s4
+ 2u(31 t
4 − 8ut3
+ 177u2t2 − 8u
3t + 660u
4)s3
+ 2u2(57t
4 − 8u t3
+ 183u2t2
+ 93u3t
+ 374u4)s2
+ u3(62t
4+ 72ut
3+ 321 u
2t2
+ 238u3t+ 264u
4)s+ 44u
4(t2
+ ut+ u2)2)
H(0, z)
}/(9st(s + t)
4u(s + u)
4(t + u)
4)
A(2)2;CF nf
= −{
8(s4
+ 2s3(t + u) + 3s
2(t2
+ u2)
+ 2s(t3
+ u3)
+(t2
+ tu + u2)2)}/(
stu)
– 16 –
A(2)
2;n2f
=
{− 18u(s + u)
4(t + u)
4(s2 − ts + t
2+ u
2)H(1, 0, y)(s + t)
5+ 6 (t + u)
4(2s
8+ 4(t + 3u)s
7+ 2
(3t
2+ 5ut + 17u
2)s6
= +(4t
3+ 15ut
2+ 6u
2t+ 60u
3)s5
+ 2(t4
+ 12u2t2 − 2 u
3t+ 36u
4)s4
+ 2u(t4 − 2ut
3+ 15u
2t2 − 2u
3t+ 30 u
4)s3
+ 2u2(3t
4 − 2ut3
+ 12u2t2
+ 3u3t+ 17u
4)s2
+(12u
7+ 10tu
6+ 15t
2u5
+ 2t4u3)s+ 2u
4(t2
+u t+u2)2)
H(0, z)(s+ t)4 − 18tu(s+u)
4(t+u)
4(t2
+ u2)H(0, y)H(0, z)(s+ t)
4 − 6(s+ u)4(2(t4
+ u t3
+ 3u2t2
+ u3t+ u
4)s4
+ 4(t5 − u2
t3 − u3
t2
+ u5)s3
+ 3(t+ u)2(2t
4+ ut
3
+ 4u2t2
+u3t+ 2u
4)s2
+ 2(t+u)3(2t
4−ut3−u3t+ 2u
4)s+ 2(t+u)
4(t2
+u t+u2)2)
H(1, z)(s+ t)4
+ 18su(s+u)4(t+u)
4(s2
+ u2)H(0, y)H(1, z)(s + t)
4 − 6(s + u)4(2(t4
+ u t3
+ 3u2t2
+ u3t + u
4)s4
+ 4(t5 − u2
t3 − u3
t2
+ u5)s3
+ 3(t + u)2(2t
4
+ ut3
+ 4u2t2
+ u3t + 2u
4)s2
+ 2(t + u)3(2t
4 − ut3 − u3t + 2u
4)s + 2(t + u)
4(t2
+ u t + u2)2)
H(2, y)(s + t)4
+ 18st(s2
+ t2)(s + u)
4(t + u)
4H(0, z)H(2, y)(s + t)
4 − 18s(s + u)4(t + u)
5(s2
+ t2
+ u2 − t u
)H(1, z)H(3, y)(s + t)
4
− 18su(s + u)4(t + u)
4(s2
+ u2)H(0, 1, z)(s + t)
4+ 18su(s + u)
4(t + u)
4(s2
+ u2)H(0, 2, y) (s + t)
4 − 18tu(s + u)4(t + u)
4(t2
+u2)H(1, 0, z)(s+ t)
4+ 18su (s+u)
4(t+u)
4(s2
+u2)H(2, 0, y)(s+ t)
4−18s(s+u)4(t+u)
5(s2
+ t2
+u2− tu
)H(3, 2, y)(s+ t)
4
+6(s+u)(t+u)(5(t+u)
3s10
+6(4t
4+15ut
3+23u
2t2
+15u3t+4u
4)s9
+(55 t
5+227ut
4+437u
2t3
+437u3t2
+227u4t+55u
5)s8
=+(80 t
6+350ut
5+731u
2t4
+940u3t3
+731u4t2
+350u5t+80u
6)s7
+(80t
7+396ut
6+852u
2t5
+1211u3t4
+1211u4t3
+852u5t2
+396u6t+80u
7)s6
+(55t
8+350ut
7+852u
2t6
+1252u3t5
+1408u4t4
+1252u5t3
+852u6t2
+350u7t+55u
8)s5
+(24t
9+227ut
8
+ 731u2t7
+ 1211u3t6
+ 1408u4t5
+ 1408u5t4
+ 1211u6t3
+ 731u7t2
+ 227u8t + 24u
9)s4
+(5t
10+ 90u t
9+ 437u
2t8
+ 940u3t7
+ 1211u4t6
+ 1252u5t5
+ 1211u6t4
+ 940u7t3
+ 437u8t2
+ 90u9t+ 5u
10)s3
+ tu(15t
9+ 138ut
8+ 437 u
2t7
+ 731u3t6
+ 852u4t5
+ 852u5t4
+ 731u6t3
+ 437u7t2
+ 138u8t+ 15u
9)s2
+ t2u2(t+ u)
2(15t
6+ 60ut
5+ 92u
2t4
+ 106u3t3
+ 92u4t2
+ 60u5t+ 15u
6)s
+ t3u3(t+u)
3(5t
4+ 9u t
3+ 13u
2t2
+ 9u3t+ 5u
4))
(s+ t) + 6(s+u)4(t+u)
4(2 s
8+ 4(3t+u)s
7+ 2(17t
2+ 5ut+ 3u
2)s6
+(60t
3
+ 6u t2
+ 15u2t + 4u
3)s5
+ 2(36t
4 − 2ut3
+ 12u2t2
+ u4)s4
+ 2t(30t
4 − 2ut3
+ 15u2t2 − 2u
3t + u
4)s3
+ 2t2(17t
4+ 3ut
3
+ 12u2t2 − 2u
3t+ 3u
4)s2
+(12t
7+ 10u t
6+ 15u
2t5
+ 2u4t3)s+ 2t
4(t2
+ ut+ u2)2)
H(0, y)
}/(9st(s + t)
4u(s + u)
4(t + u)
4)
A(2)
3;C2A
={
49s4
+ 98s3
(t + u) + 147s2(t2
+ u2)
+ 98s(t3
+ u3)
+ 49t4 − 450t
3u + 165t
2u2 − 450tu
3+ 49u
4}/(
5stu)
A(2)3;CAnf
={
353t2 − 588tu + 353u
2}/(
5s)
A(2)3;CF nf
= −18{t2
+ u2}/(
s)
A(2)
3;n2f
= 0
A(2)
4;C2A
=
{9s
2t2u2(231s
16+ 1896(t + u)s
15+ 6
(1205t
2+ 2582u t + 1205u
2)s14
+ 2(8485t
3+ 28497ut
2+ 28497u
2t + 8485 u
3)s13
= +(27247t
4+ 132002ut
3+ 187458u
2t2
+ 132002u3t+ 27247u
4)s12
+ 12(2609t
5+ 18137ut
4+ 32471u
2t3
+ 32471 u3t2
+ 18137u4t
+2609u5)s11
+(26071t
6+265278u t
5+584223u
2t4
+758272u3t3
+584223u4t2
+265278u5t+26071 u
6)s10
+2(7765t
7+118994ut
6
+329001u2t5
+544812u3t4
+544812u4t3
+329001u5t2
+118994u6t+7765u
7)s9
+3(2110t
8+50618ut
7+186907u
2t6
+405032u3t5
+ 468376u4t4
+ 405032u5t3
+ 186907u6t2
+ 50618u7t+ 2110u
8)s8
+ 4(398t
9+ 16089ut
8+ 86178u
2t7
+ 272710u3t6
+ 333261u4t5
+ 333261 u5t4
+ 272710u6t3
+ 86178u7t2
+ 16089u8t+ 398u
9)s7
+(187t
10+ 16046ut
9+ 137715u
2t8
+ 724384u3t7
+ 1065452u4t6
+947616u5t5
+1065452u6t4
+724384u7t3
+137715u8t2
+16046u9t+187u
10)s6
+6tu(299t
9+5160ut
8+51597u
2t7
+106788 u3t6
+101934u4t5
+101934u5t4
+106788u6t3
+51597u7t2
+5160u8t+299u
9)s5
+t2u2(2973t
8+74726ut
7+236013u
2t6
+329784u3t5
+314484u4t4
+329784u5t3
+236013u6t2
+74726u7t+2973u
8)s4
+12t3u3(651t
7+3762ut
6+9502u
2t5
+11138 u3t4
+11138u4t3
+ 9502u5t2
+ 3762u6t + 651u
7)s3
+ 3t4u4(1027t
6+ 7446ut
5+ 12323u
2t4
+ 11392u3t3
+ 12323u4t2
+ 7446u5t + 1027u
6)s2
+ 6t5u5(315t
5+ 904ut
4+ 837u
2t3
+ 837u3t2
+ 904u4t+ 315u
5)s+ t
6u6(215t
4+ 250ut
3+ 357u
2t2
+ 250u3t+ 215u
4))
(t+ u)6
=− 108s2t2(s+ t)
6u2(s+ u)
6(s4
+ 2(t+ u)s3
+ 3(t2
+ u2)s2
+ 2(t3
+ u3)s+ t
4+ u
4 − 12tu3
+ 18t2u2 − 24t
3u)H(0, y)(t+ u)
6
− 108s2t2
(s+ t)6u2(s+ u)
6(s4
+ 2(t+ u)s3
+ 3(t2
+ u2)s2
+ 2(t3
+ u3)s+ t
4+ u
4 − 24tu3
+ 18t2u2 − 12t
3u)H(0, z) (t+ u)
6
+216s2t2(s+ t)
6u3(s+u)
6(2s
3−6us2
+10u2s+3t
(2t
2−3ut+4u2))H(1, y)(t+u)
6+108s
2t2(s+ t)
6u2
(s+u)6(s4
+2(t−u)s3
+ 3(t2
+ 5u2)s2
+ 2(t3 − 9 u
3)s+ t
4+ u
4+ 18tu
3 − 9t2u2
+ 30t3u)H(1, z)(t+ u)
6+ 108 s
2t2(s+ t)
6u2(s+ u)
6(s4 − 2(t+ u)s
3
+ 15(t2
+ u2)s2 − 18
(t3
+ u3)s + t
4+ u
4+ 6tu
3+ 9t
2u2
+ 6t3u)H(2, y)(t + u)
6
}/(27s
3t3u3(s + t)
6(s + u)
6(t + u)
6)
– 17 –
A(2)4;CAnf
=
{9s
2t2u2(54s
16+ 420(t + u)s
15+ 24
(64t
2+ 93ut + 64 u
2)s14
+(3520t
3+ 6099ut
2+ 6099u
2t + 3520u
3)s13
= + 2(2821t
4+ 4943ut
3+ 9330u
2t2
+ 4943u3t+ 2821u
4)s12
+ 6(1106t
5+ 1697ut
4+ 6163u
2t3
+ 6163u3t2
+ 1697u4t+ 1106 u
5)s11
+(5810t
6+7365ut
5+65076u
2t4
+38726u3t3
+65076u4t2
+7365u5t+5810u
6)s10
+(3736t
7+3503u t
6+105864u
2t5
+17977u3t4
+17977u4t3
+105864u5t2
+3503u6t+3736u
7)s9
+3(560t
8+208ut
7+38974u
2t6
+8059u3t5−15308u
4t4
+8059u5t3
+38974u6t2
+ 208u7t + 560u
8)s8
+(472t
9+ 60ut
8+ 81318u
2t7 − 8215u
3t6
+ 18453u4t5
+ 18453 u5t4 − 8215u
6t3
+ 81318u7t2
+ 60u8t
+ 472u9)s7
+(62 t
10+ 229ut
9+ 37632u
2t8 − 50045u
3t7
+ 25292u4t6
+ 177060u5t5
+ 25292u6t4 − 50045u
7t3
+ 37632u8t2
+ 229u9t + 62u
10)s6
+ 3tu(24t
9+ 3679ut
8 − 12820u2t7
+ 195u3t6
+ 50191u4t5
+ 50191u5t4
+ 195u6t3 − 12820u
7t2
+ 3679u8t
+ 24u9)s5
+ 2 t2u2(735t
8 − 6322ut7
+ 3033u2t6
+ 30537u3t5
+ 41982u4t4
+ 30537u5t3
+ 3033u6t2 − 6322u
7t + 735u
8)s4
+ t3u3(− 1700t
7+ 5703ut
6+ 17862u
2t5
+ 21167u3t4
+ 21167u4t3
+ 17862 u5t2
+ 5703u6t− 1700u
7)s3
+ 12t4u4(109t
6
+ 190u t5
+ 297u2t4
+ 423u3t3
+ 297u4t2
+ 190u5t + 109u
6)s2 − 6t
5u5(12t
5 − 24ut4 − 209u
2t3 − 209u
3t2 − 24u
4t + 12u
5)s
= + t6u6(20t
4+ 131ut
3+ 174u
2t2
+ 131u3t + 20u
4))
(t + u)6 − 162s
2t3(s + t)
6u3(s + u)
6(8t
2 − 21ut
+ 17u2)H(0, y)(t + u)
6 − 162s2t3(s + t)
6u3(s + u)
6(17t
2 − 21ut + 8 u2)H(0, z)(t + u)
6 − 54s2t2(s + t)
6u3(s + u)
6(41s
3
− 42u s2
+ 5u2s + t
(50t
2 − 63ut + 23u2))H(1, y)(t + u)
6+ 54s
2t2(s + t)
6u3(s + u)
6(41s
3 − 42us2
+ 5u2s + t
(− 25t
2+ 63u t− 52u
2))H(1, z)(t + u)
6+ 54s
2t2(s + t)
6u2(s + u)
6(41(t + u)s
3 − 42(t2
+ u2)s2
+ 5(t3
+ u3)s− 2t u
(t2
+ u2))H(2, y)(t + u)
6
}/(27s
3t3u3(s + t)
6(s + u)
6(t + u)
6)
A(2)4;CF nf
=
{432s
3t2(s+ t)
6u2(s+u)
6(− 3s
2+ t
2+u
2− tu)H(2, y) (t+u)
7− 18s2t2u2(48s
16+ 384(t+u)s
15+ 12
(120t
2+ 227 ut
= + 120u2)s14
+(3360t
3+ 9087ut
2+ 9087u
2t + 3360 u
3)s13
+ 3(1808t
4+ 6521ut
3+ 8604u
2t2
+ 6521u3t + 1808 u
4)s12
+(6336t
5+ 30735ut
4+ 47598u
2t3
+ 47598u3t2
+ 30735u4t + 6336u
5)s11
+(5424t
6+ 36543ut
5+ 67614u
2t4
+ 73464u3t3
+ 67614u4t2
+ 36543u5t + 5424u
6)s10
+(3360t
7+ 32505ut
6+ 77922u
2t5
+ 91295u3t4
+ 91295u4t3
+ 77922u5t2
+ 32505u6t
+ 3360u7)s9
+ 3(480t
8+ 6939u t
7+ 23404u
2t6
+ 34497u3t5
+ 31012u4t4
+ 34497u5t3
+ 23404u6t2
+ 6939u7t + 480u
8)s8
+ 3(128t
9+ 2999ut
8+ 15226u
2t7
+ 33508u3t6
+ 30137u4t5
+ 30137u5t4
+ 33508u6t3
+ 15226u7t2
+ 2999u8t + 128u
9)s7
+(48t
10+ 2337ut
9+ 19494u
2t8
+ 70630u3t7
+ 86678u4t6
+ 65250u5t5
+ 86678u6t4
+ 70630u7t3
+ 19494u8t2
+ 2337u9t
+ 48u10)s6
+ 3tu(92t
9+ 1601u t
8+ 10417u
2t7
+ 20343u3t6
+ 17708u4t5
+ 17708u5t4
+ 20343u6t3
+ 10417u7t2
+ 1601u8t
+ 92u9)s5
+ 3t2u2(172t
8+ 2556 ut
7+ 8524u
2t6
+ 11797u3t5
+ 10692u4t4
+ 11797u5t3
+ 8524u6t2
+ 2556u7t + 172u
8)s4
+ t3u3(788t
7+ 5538ut
6+ 14103u
2t5
+ 16252u3t4
+ 16252u4t3
+ 14103u5t2
+ 5538u6t + 788u
7)s3
+ 3t4u4(148t
6
+ 959ut5
+ 1726u2t4
+ 1748u3t3
+ 1726u4t2
+ 959u5t + 148u
6)s2
+ 3t5u5(72t
5+ 265ut
4+ 347u
2t3
+ 347u3t2
+ 265u4t
+ 72u5)s + 2t
6u6(16t
4+ 39ut
3+ 54 u
2t2
+ 39u3t + 16u
4))
(t + u)6
+ 108s2t3(s + t)
6u3
(s + u)6(t2
+ 13u2)H(0, y)(t + u)
6
+ 108s2t3(s + t)
6u3
(s + u)6(13t
2+ u
2)H(0, z)(t + u)
6+ 108s
2t2(s + t)
6u3
(s + u)6(12s
3 − 4u2s + 13t
3+ tu
2)H(1, y)(t + u)
6
− 108s2t2
(s + t)6u3(s + u)
6(12s
3 − 4u2s− t
(t2
+ 13u2))
H(1, z)(t + u)6
}/(27s
3t3u3(s + t)
6(s + u)
6(t + u)
6)
A(2)
4;n2f
= 0
A(2)
5;C2A
=
{9s
2t2(s + t)
2u2(55s
14+ (330t + 416u)s
13+(935 t
2+ 1844ut + 1500u
2)s12
+ 30(55t
3+ 135ut
2+ 167u
2t + 115 u
3)s11
= +(1980t
4+ 5670ut
3+ 8826u
2t2
+ 8462u3t + 5643 u
4)s10
+ 2(825t
5+ 2487ut
4+ 6495u
2t3
+ 3799u3t2
+ 5061 u4t + 3426u
5)s9
+(935t
6+2568ut
5+15141u
2t4
+4070u3t3−1902u
4t2
+9678u5t+6231u
6)s8
+2(165t
7+443u t
6+6261u
2t5−139u
3t4−8575u
4t3
− 4065u5t2
+ 3881u6t + 2085 u
7)s7
+(55t
8+ 334ut
7+ 7728u
2t6 − 6262u
3t5 − 17396u
4t4 − 22194u
5t3 − 7172u
6t2
+ 5130u7t
+ 1950u8)s6
+ 2u(45 t
8+ 1695ut
7 − 3483u2t6 − 4305u
3t5 − 4851u
4t4 − 8249u
5t3 − 1455u
6t2
+ 1362u7t+ 284u
8)s5
+ u2(717t
8
− 2782ut7 − 1182u
2t6
+ 5322u3t5 − 4938u
4t4 − 7502u
5t3
+ 711u6t2
+ 998u7t + 77 u
8)s4 − 2tu
3(158t
7 − 735ut6 − 2541u
2t5
−2255u3t4
+577 u4t3
+150u5t2−512u
6t−82u
7)s3
+t2u4(717t
6+1098u t
5+2632u
2t4
+2622u3t3
+1308u4t2
+852u5t+234u
6)s2
+2 t3u5(45t
5+157ut
4+619u
2t3
+516u3t2
+340u4t+102 u
5)s+t
4u6(55t
4+134ut
3+207u
2t2
+134u3t+105 u
4))H(0, y)(t+u)
6
– 18 –
= + 9s2t2u2(s+u)
2(55s
14+ (416 t+ 330u)s
13+(1500t
2+ 1844ut+ 935u
2)s12
+ 30(115 t
3+ 167ut
2+ 135u
2t+ 55u
3)s11
+(5643t
4
+ 8462ut3
+ 8826 u2t2
+ 5670u3t + 1980u
4)s10
+ 2(3426t
5+ 5061ut
4+ 3799 u
2t3
+ 6495u3t2
+ 2487u4t + 825u
5)s9
+(6231t
6
+ 9678u t5 − 1902u
2t4
+ 4070u3t3
+ 15141u4t2
+ 2568u5t + 935u
6)s8
+ 2(2085t
7+ 3881ut
6 − 4065u2t5 − 8575u
3t4 − 139u
4t3
+ 6261u5t2
+ 443u6t + 165u
7)s7
+(1950t
8+ 5130ut
7 − 7172u2t6 − 22194u
3t5 − 17396u
4t4 − 6262u
5t3
+ 7728u6t2
+ 334u7t
+ 55 u8)s6
+ 2t(284t
8+ 1362ut
7 − 1455u2t6 − 8249u
3t5 − 4851 u
4t4 − 4305u
5t3 − 3483u
6t2
+ 1695u7t + 45u
8)s5
+ t2(77 t
8
+998ut7
+711u2t6−7502u
3t5−4938u
4t4
+5322u5t3−1182u
6t2−2782u
7t+717u
8)s4
+2t3u(82t
7+512ut
6−150u2t5−577u
3t4
+ 2255u4t3
+ 2541u5t2
+ 735u6t− 158u
7)s3
+ t4u2(234t
6+ 852ut
5+ 1308u
2t4
+ 2622u3t3
+ 2632u4t2
+ 1098u5t + 717u
6)s2
+2t5u3(102t
5+340ut
4+516u
2t3
+619u3t2
+157u4t+45u
5)s+t
6u4(105t
4+134ut
3+207u
2t2
+134u3t+55u
4))H(0, z)(t+u)
6
+108s2t2(s+t)
6u2
(s+u)6(3s
4+6(t+u)s
3+9(t2
+u2)s2
+6(t3
+u3)s+3t
4+3u
4−4tu3−6t
2u2−4t
3u)H(0, y) H(0, z)(t+u)
6
−18s2t2(s+ t)
2u2(s+u)
6(3s
8+2(51t+u) s
7+(486t
2+200ut+30u
2)s6
+6(179t
3+130ut
2+96u
2t+7u
3)s5
+2(687t
4+677ut
3
+ 945u2t2
+ 265u3t+ 29 u
4)s4
+ 2t(537t
4+ 677ut
3+ 1344u
2t2
+ 658u3t+ 170 u
4)s3
+ 2t2(243t
4+ 390ut
3+ 945u
2t2
+ 658u3t
+ 270 u4)s2
+ 2t3(51t
4+ 100ut
3+ 288u
2t2
+ 265u3t + 170 u
4)s + t
4(3t
4+ 2ut
3+ 30u
2t2
+ 42u3t + 58 u
4))H(1, y)(t + u)
6
=− 216s2t2(s + t)
6u3(s + u)
6(2 s
3 − 3us2
+ 4u2s + t
(2t
2 − 3ut + 4u2))H(0, z)H(1, y) (t + u)
6 − 108s2t2(s + t)
6u2(s + u)
6(3s
4
+ (6t− 8u)s3
+(9 t
2+ 6u
2)s2
+(6t
3 − 4u3)s + 3t
4+ 3u
4+ 12tu
3+ 6t
2u2
+ 16t3u)H(0, y)H(1, z)(t + u)
6
−1296s2t2(s+t)
6u3(s+u)
6(s3−us2 +u
2s+t
(t2−ut+u2
))H(1, y)H(1, z) (t+u)
6−108s2t2(s+t)
6u2(s+u)
6(3s
4+(2u−8t)s
3
+ 3(2 t
2+ 5u
2)s2 − 2
(2t
3+ u
3)s+ 3t
4+ 3u
4+ 8tu
3+ 12t
2u2
+ 8t3u)H(0, z)H(2, y)(t+ u)
6 − 108s2t2(s+ t)
6u2(s+ u)
6(8s
4
+(4t−2u)s3
+9(2t
2+3u
2)s2−2u
3s+8t
4+8 u
4+18tu
3+27t
2u2
+18t3u)H(1, z)H(2, y)(t+u)
6−108s2t2
(s+t)6u2(s+u)
6(2s
4
+ 10(t + u)s3 − 3
(t2
+ u2)s2
+ 6(t3
+ u3)s + 2
(t2
+ ut + u2)2)
H(1, z)H(3, y) (t + u)6 − 108s
2t3(s + t)
6u3(s + u)
6(6t
2 − 9ut
+ 2u2)H(0, 0, y)(t + u)
6 − 108s2t3(s + t)
6u3(s + u)
6(2t
2 − 9ut + 6 u2)H(0, 0, z)(t + u)
6+ 432s
2t2(s + t)
6u2(s + u)
6(2s
4
+2(2 t+u)s3
+3(2t
2+u
2)s2
+2(2t
3+u
3)s+2t
4+2 u
4+2tu
3+3t
2u2
+2t3u)H(0, 1, y)(t+u)
6+108s
2t2(s+ t)
6u2(s+u)
6(3s
4
+(6t−2u)s3
+3(3t
2+5u
2)s2
+2(3t
3+u
3)s+3t
4+3u
4−14tu3
+9t2u2−14t
3u)H(0, 1, z)(t+u)
6−108s2t2(s+t)
6u2(s+u)
6(3s
4
+8(t−u)s3
+6(2t
2+u
2)s2
+(8t
3−4u3)s+3
(t4
+6u t3−u2
t2
+6u3t+u
4))H(0, 2, y)(t+u)
6+108s
2t2(s+ t)
6u2(s+u)
6(6s
4
=+2(6t−u)s3
+3(6t
2+5u
2)s2
+2(6t
3+u
3)s+6t
4+6u
4+6tu
3+9t
2u2
+6t3u)H(1, 0, y)(t+u)
6+108s
2t2(s+t)
6u2(s+u)
6(3s
4
+2(3t+5u) s3
+3(3t
2+u
2)s2
+2(3t
3+7u
3)s+3t
4+3u
4−2 tu3−3t
2u2−2t
3u)H(1, 0, z)(t+u)
6+216s
2t2(s+t)
6u2
(s+u)6(4s
4
+8(t+u)s3
+3(4t
2+u
2)s2
+(8t
3+6 u
3)s+4t
4+4u
4+6tu
3+3t
2u2
+8t3u)H(1, 1, y) (t+u)
6+108s
2t2(s+ t)
6u3(s+u)
6(18s
3
− 3us2
+ 18u2s− t
(18t
2+ 9ut + 14u
2))H(1, 1, z)(t + u)
6 − 1296s2t2
(s + t)6u3(s + u)
6(s3 − us2 + u
2s + t
(t2 − ut
+ u2))
H(1, 2, y)(t + u)6 − 108s
2t2(s + t)
6u2(s + u)
6(3s
4+ 2(t− 4u)s
3+ 3
(5t
2+ 2u
2)s2 − 2
(t3
+ 2u3)s + 3t
4+ 3u
4+ 8t u
3
+ 12t2u2
+ 8t3u)H(2, 0, y)(t + u)
6 − 108s2t2(s + t)
6u3
(s + u)6(6s
3 − 9us2
+ 2u2s + t
(2t
2+ 3ut + 2u
2))
H(2, 1, y)(t + u)6
− 108s2t2(s + t)
6u2(s + u)
6(8s
4 − 2(t + u)s3
+ 27(t2
+ u2)s2 − 2
(t3
+ u3)s + 8
(t2
+ u t + u2)2)
H(2, 2, y)(t + u)6
− 108s2t2(s + t)
6u2(s + u)
6(2s
4+ 10(t + u)s
3 − 3(t2
+ u2)s2
+ 6(t3
+ u3)s + 2
(t2
+ ut + u2)2)
H(3, 2, y)(t + u)6
= + 9t2(s+ t)u
2(s+u)
(366(t+u)
6s16
+ 12(213t
7+ 1475ut
6+ 4463u
2t5
+ 7365u3t4
+ 7365u4t3
+ 4463u5t2
+ 1475u6t+ 213u
7)s15
+2(t+u)2(4186t
6+23989ut
5+61240u
2t4
+77078u3t3
+61240u4t2
+23989 u5t+4186u
6)s14
+2(8526t
9+72111ut
8+283103u
2t7
+ 646677u3t6
+ 948359u4t5
+ 948359u5t4
+ 646677u6t3
+ 283103u7t2
+ 72111u8t+ 8526u
9)s13
+ (t+ u)2(23886t
8+ 172264u t
7
+ 582649u2t6
+ 1131132u3t5
+ 1344162u4t4
+ 1131132u5t3
+ 582649 u6t2
+ 172264u7t+ 23886u
8)s12
+(23866t
11+ 243086u t
10
+ 1157425u2t9
+ 3382695u3t8
+ 6575795u4t7
+ 8973837u5t6
+ 8973837u6t5
+ 6575795u7t4
+ 3382695u8t3
+ 1157425u9t2
+ 243086 u10t + 23866u
11)s11
+ (t + u)2(17016t
10+ 164440u t
9+ 724400u
2t8
+ 1917401u3t7
+ 3236864u4t6
+ 3710558u5t5
+ 3236864 u6t4
+ 1917401u7t3
+ 724400u8t2
+ 164440u9t+ 17016u
10)s10
+ 2(4176t
13+ 58901ut
12+ 382615u
2t11
+ 1458232u3t10
+ 3634444u4t9
+ 6299163u5t8
+ 8074581u6t7
+ 8074581u7t6
+ 6299163u8t5
+ 3634444u9t4
+ 1458232u10t3
+ 382615u11
t2
+ 58901u12t + 4176u
13)s9
+ (t + u)2(2552t
12+ 42616u t
11+ 321337u
2t10
+ 1192960u3t9
+ 2636700u4t8
+ 3851544u5t7
+ 4187542u6t6
+ 3851544u7t5
+ 2636700u8t4
+ 1192960u9t3
+ 321337 u10t2
+ 42616u11t + 2552u
12)s8
+(366t
15+ 11590u t
14
+ 150117u2t13
+ 868535u3t12
+ 2906129u4t11
+ 6451075u5t10
+ 10280514u6t9
+ 12609962u7t8
+ 12609962u8t7
+ 10280514u9t6
– 19 –
= + 6451075u10t5
+ 2906129u11t4
+ 868535u12t3
+ 150117u13
t2
+ 11590u14t + 366u
15)s7
+ tu(t + u)2(1254t
12+ 30458 ut
11
+192025u2t10
+634366u3t9
+1369170u4t8
+2072140u5t7
+2324670u6t6
+2072140u7t5
+1369170u8t4
+634366u9t3
+192025 u10t2
+30458u11t+1254u
12)s6
+2t2u2(1605 t
13+19222ut
12+110551u
2t11
+398318u3t10
+989437u4t9
+1764628u5t8
+2329703u6t7
+ 2329703u7t6
+ 1764628u8t5
+ 989437 u9t4
+ 398318u10t3
+ 110551u11t2
+ 19222u12t + 1605 u
13)s5
+ t3u3(t + u)
2(1678t
10
+19862ut9
+93582u2t8
+253073u3t7
+439352u4t6
+520162u5t5
+439352u6t4
+253073u7t3
+93582u8t2
+19862u9t+1678u
10)s4
+ t4u4(t + u)
3(1260t
8+ 9096ut
7+ 30583u
2t6
+ 61244u3t5
+ 75426u4t4
+ 61244 u5t3
+ 30583u6t2
+ 9096u7t + 1260u
8)s3
+ t5u5(t+u)
4(324t
6+ 2168ut
5+ 6197u
2t4
+ 8622u3t3
+ 6197u4t2
+ 2168u5t+ 324u
6)s2
+ 10t6u6(t+u)
7(14t
2+ 27ut+ 14u
2)s
+40t7u7(t+u)
6(t2
+ut+u2))
+9s2t2u2(3(11t
6+130ut
5+141u
2t4
+604u3t3
+141u4t2
+130u5t+11 u
6)s16
+8(45t
7+521ut
6
+ 1056u2t5
+ 2598u3t4
+ 2488 u4t3
+ 858u5t2
+ 411u6t + 23u
7)s15
+ 6(285t
8+ 3120u t
7+ 8470u
2t6
+ 17852u3t5
+ 25104u4t4
= + 15024u5t3
+ 5642u6t2
+ 1908 u7t + 83u
8)s14
+ 2(2375t
9+ 24561ut
8+ 80646u
2t7
+ 164370 u3t6
+ 268500u4t5
+ 242676u5t4
+112746u6t3
+43806u7t2
+11685u8t+539u
9)s13
+(8669t
10+85044ut
9+320811u
2t8
+677420 u3t7
+1161930u4t6
+1394268u5t5
+895510u6t4
+373044u7t3
+149697 u8t2
+34384u9t+2343u
10)s12
+12(915t
11+8573u t
10+35593u
2t9
+81037u3t8
+140831u4t7
+205671u5t6
+184091u6t5
+94279u7t4
+41772u8t3
+16990u9t2
+3718u10t+370 u
11)s11
+(9845t
12+88872ut
11+394182u
2t10
+982076u3t9
+1680477u4t8
+2723040u5t7
+3377880u6t6
+2469456u7t5
+1323771u8t4
+704312u9t3
+264210u10t2
+55188 u11t
+ 6179u12)s10
+ 2(3095t
13+ 27024ut
12+ 127632 u
2t11
+ 352506u3t10
+ 563960u4t9
+ 824355u5t8
+ 1409056u6t7
+ 1665520u7t6
+ 1351875u8t5
+ 966790u9t4
+ 514400u10t3
+ 159702 u11t2
+ 28798u12t + 2919u
13)s9
+ 3(870t
14+ 7314u t
13+ 37677u
2t12
=+112780u3t11
+143003u4t10
+53282u5t9
+249844u6t8
+845260u7t7
+1239890u8t6
+1252614u9t5
+905087 u10t4
+401760u11t3
+ 101733u12t2
+ 14670u13t + 1176 u
14)s8
+ 4(166t
15+ 1359ut
14+ 8343u
2t13
+ 18170u3t12 − 29355u
4t11 − 193428u
5t10
− 186082u6t9
+ 373479u7t8
+ 1074360u8t7
+ 1349559u9t6
+ 1156713u10t5
+ 673434u11t4
+ 244731u12t3
+ 51600u13t2
+ 5604u14t
+ 307u15)s7
+(77t
16+ 712ut
15+ 7926u
2t14 − 22420u
3t13 − 310304u
4t12 − 964008u
5t11 − 1004190u
6t10
+ 1290836u7t9
+ 5018184u8t8
+ 6920472u9t7
+ 6102774u10t6
+ 3900588u11t5
+ 1764592u12
t4
+ 528392u13t3
+ 92178u14t2
+ 6772u15t
+ 187u16)s6
+ 6 tu(5t
15+ 338ut
14 − 3532u2t13 − 33260u
3t12 − 97374u
4t11 − 95800u
5t10
+ 181294u6t9
+ 739773u7t8
+ 1163599u8t7
+ 1123652u9t6
+ 758126u10t5
+ 368632u11t4
+ 127306u12t3
+ 29970u13t2
+ 4032u14t+ 151u
15)s5
+ t2u2(327 t
14
− 6804ut13 − 59454u
2t12 − 167472u
3t11 − 99128u
4t10
+ 699492u5t9
+ 2552097u6t8
+ 4572060u7t7
+ 5195055u8t6
+ 4069272u9t5
+ 2242188u10t4
+ 847572u11t3
+ 212250u12t2
+ 33688u13t+ 2793u
14)s4
+ 4t3u3(− 233t
13− 1616u t12− 3051u
2t11
+ 10663u3t10
= + 80192u4t9
+ 249270u5t8
+ 483611 u6t7
+ 633999u7t6
+ 583800u8t5
+ 382847u9t4
+ 174178u10t3
+ 51444 u11t2
+ 8727u12t
+ 617u13)s3
+ 3t4u4(t + u)
2(109 t
10+ 662ut
9+ 4205u
2t8
+ 17972u3t7
+ 46152u4t6
+ 74668u5t5
+ 76440u6t4
+ 53188u7t3
+ 24579u8t2
+ 6934u9t + 931u
10)s2
+ 2t5u5(t + u)
3(15t
8+ 481ut
7+ 3156u
2t6
+ 8739u3t5
+ 13780 u4t4
+ 12711u5t3
+ 7500u6t2
+ 2637u7t + 453u
8)s + t
6u6
(t + u)6(77t
4+ 270ut
3+ 477u
2t2
+ 350u3t + 187u
4))
H(1, z) + 9s2t2u2(3(13t
6
+ 142ut5
+ 171u2t4
+ 644u3t3
+ 171u4t2
+ 142u5t + 13u
6)s16
+ 8(50t
7+ 578ut
6+ 1293 u
2t5
+ 3103u3t4
+ 3103u4t3
+ 1293u5t2
+ 578u6t+ 50u
7)s15
+ 12(157t
8+ 1789ut
7+ 5420u
2t6
+ 12039u3t5
+ 17342u4t4
+ 12039u5t3
+ 5420u6t2
+ 1789u7t
+ 157u8)s14
+(5374 t
9+ 59826ut
8+ 223092u
2t7
+ 513996u3t6
+ 871536u4t5
+ 871536u5t4
+ 513996u6t3
+ 223092u7t2
+ 59826u8t + 5374u
9)s13
+(10359t
10+ 114484ut
9+ 503079u
2t8
+ 1279432u3t7
+ 2390090u4t6
+ 3044424u5t5
+ 2390090u6t4
+ 1279432u7t3
+ 503079 u8t2
+ 114484u9t + 10359u
10)s12
+ 12(1186t
11+ 13429u t
10+ 67778u
2t9
+ 197005u3t8
+ 403359u4t7
+ 605123u5t6
+ 605123u6t5
+ 403359u7t4
+ 197005u8t3
+ 67778u9t2
+ 13429u10t + 1186 u
11)s11
+(14195t
12+ 171720ut
11
+ 991722u2t10
+ 3343932u3t9
+ 7591317u4t8
+ 12777132u5t7
+ 15424700u6t6
+ 12777132u7t5
+ 7591317u8t4
+ 3343932u9t3
+ 991722u10
t2
+ 171720u11t + 14195u
12)s10
+ 2(5067t
13+ 68848u t
12+ 464430u
2t11
+ 1834210u3t10
+ 4687302u4t9
+ 8645967u5t8
+ 11943168u6t7
+ 11943168u7t6
+ 8645967u8t5
+ 4687302u9t4
+ 1834210u10t3
+ 464430u11t2
+ 68848u12t
+ 5067u13)s9
+ 3(1638t
14+ 26822ut
13+ 219527u
2t12
+ 1022692u3t11
+ 2994269u4t10
+ 6115342u5t9
+ 9403374u6t8
– 20 –
= + 10916304u7t7
+ 9403374u8t6
+ 6115342u9t5
+ 2994269u10t4
+ 1022692u11
t3
+ 219527u12t2
+ 26822u13t + 1638u
14)s8
+ 4(361 t
15+ 8109ut
14+ 85470u
2t13
+ 471328u3t12
+ 1600674u4t11
+ 3733632u5t10
+ 6488383u6t9
+ 8627643u7t8
+ 8627643u8t7
+ 6488383u9t6
+ 3733632u10t5
+ 1600674u11t4
+ 471328u12
t3
+ 85470u13t2
+ 8109u14t + 361u
15)s7
+(193 t
16+ 8108ut
15
+ 123366u2t14
+ 816896u3t13
+ 3259172u4t12
+ 8952972u5t11
+ 18149594u6t10
+ 27988696u7t9
+ 32478774u8t8
+ 27988696u9t7
+ 18149594u10t6
+ 8952972u11t5
+ 3259172u12t4
+ 816896u13t3
+ 123366u14t2
+ 8108u15t+ 193u
16)s6
+ 6tu(157t
15+ 4612ut
14
+ 39024u2t13
+ 191670u3t12
+ 643658u4t11
+ 1557030u5t10
+ 2799334u6t9
+ 3770803u7t8
+ 3770803u8t7
+ 2799334u9t6
+ 1557030u10t5
+ 643658u11t4
+ 191670u12t3
+ 39024u13t2
+ 4612u14t+ 157u
15)s5
+ t2u2(2883t
14+ 38608ut
13+ 269730u
2t12
+ 1182108u3t11
+ 3470348u4t10
+ 7219608u5t9
+ 11105895u6t8
+ 12818744u7t7
+ 11105895u8t6
+ 7219608u9t5
+ 3470348u10t4
+ 1182108u11t3
+ 269730u12t2
+ 38608u13t+ 2883u
14)s4
+ 4t3u3(647t
13+ 9737ut
12+ 60783u
2t11
+ 220492u3t10
+ 533350u4t9
+ 931704u5t8
+ 1224463u6t7
+ 1224463u7t6
+ 931704u8t5
+ 533350u9t4
+ 220492u10t3
+ 60783u11t2
+ 9737u12t + 647u
13)s3
+ 3 t4u4(t+ u)
2(961t
10+ 7506ut
9+ 28145u
2t8
+ 66084u3t7
+ 107838u4t6
+ 127716u5t5
+ 107838u6t4
+ 66084u7t3
+ 28145u8t2
+ 7506u9t + 961u
10)s2
+ 6t5u5(t + u)
3(157t
8+ 937u t
7+ 2766u
2t6
+ 5043u3t5
+ 6226u4t4
+ 5043u5t3
+ 2766u6t2
+ 937u7t
+ 157u8)s + t
6u6(t + u)
6(193t
4+ 354ut
3+ 537u
2t2
+ 354 u3t + 193u
4))H(2, y)
}/(27s
3t3u3(s + t)
6(s + u)
6(t + u)
6)
A(2)5;CAnf
=
{216s
2t2u3(s+u)
6(t+u)
6(s2−ts+t
2+u
2)H(0, 1, y) (s+t)
7+162s
2t3u3(s+u)
6(t+u)
6(t2
+u2)H(0, y)H(0, z) (s+t)
6
= + 54s2t2u3(s+u)
6(t+u)
6(16s
3 − 21us2
+ 7u2s+ t
(16t
2 − 21ut+ 7u2))H(0, z)H(1, y)(s+ t)
6 − 54s2t2u3
(s+u)6(t+u)
6(10s
3
− 21us2
+ 19u2s + t
(− 8t
2+ 21ut− 17 u
2))H(0, y)H(1, z)(s + t)
6+ 1134s
2t2u3(s + u)
6(t + u)
6(s3 − 2us
2
+ u2s + t(t− u)
2)H(1, y)H(1, z)(s + t)
6+ 54s
2t2u2(s + u)
6(t + u)
6(− 2(5t + 8u)s
3+ 21
(t2
+ u2)s2 −
(19t
3
+ 7u3)s + tu
(t2
+ u2))H(0, z) H(2, y)(s + t)
6+ 54s
2t2u2(s + u)
6(t + u)
6(− 4(5t + 6u)s
3+ 21
(t2
+ 2u2)s2
−(11t
3+ 24u
3)s + tu
(t2
+ u2))H(1, z)H(2, y)(s + t)
6+ 162s
3t2u2(s + u)
6(t + u)
6(2(t + u)s
2 − 7(t2
+ u2)s + 5
(t3
+ u3))H(1, z)H(3, y)(s + t)
6+ 162s
2t3u3(s + u)
6(t + u)
6(2t
2 − 7ut + 5u2)H(0, 0, y)(s + t)
6
= + 162s2t3u3
(s+u)6(t+u)
6(5t
2 − 7ut+ 2u2)H(0, 0, z)(s+ t)
6+ 54s
2t2u3(s+u)
6(t+u)
6(7s
3 − 21us2
+ 16u2s+ t
(25t
2 − 42ut
+ 25 u2))H(0, 1, z)(s + t)
6+ 54s
2t2u2(s + u)
6(t + u)
6((t− 10u)s
3+ 21u
2s2
+(t3 − 19u
3)s + 21t(t− u)
2u)H(0, 2, y)(s + t)
6
+ 54s2t2u3(s+ u)
6(t+ u)
6(10s
3 − 21u s2
+ 19u2s+ t
3+ tu
2)H(1, 0, y)(s+ t)
6 − 54s2t2u3(s+ u)
6(t+ u)
6(16s
3 − 21us2
+ 7u2s
− 2t(t2
+ u2))
H(1, 0, z)(s + t)6 − 54s
2t2u3(s + u)
6(t + u)
6(s3 − 21us
2+ 10u
2s + t
(t2 − 21ut + 10u
2))H(1, 1, y)(s + t)
6
− 162s2t2u3
(s + u)6(t + u)
6(8s
3 − 14us2
+ 8u2s + t
(− 4t
2+ 7ut− 7 u
2))H(1, 1, z)(s + t)
6+ 1134s
2t2u3(s + u)
6(t + u)
6(s3
− 2us2
+ u2s + t(t− u)
2)H(1, 2, y)(s + t)
6+ 54s
2t2u2
(s + u)6(t + u)
6(− 2(8t + 5u)s
3+ 21
(t2
+ u2)s2 −
(7 t
3
+ 19u3)s + tu
(t2
+ u2))H(2, 0, y)(s + t)
6+ 54s
2t2u3(s + u)
6(t + u)
6(4s
3 − 21us2
+ 13u2s + t
3+ tu
2)H(2, 1, y)(s + t)
6
− 324s3t2u2(s + u)
6(t + u)
6(4(t + u)s
2 − 7(t2
+ u2)s + 4
(t3
+ u3))H(2, 2, y)(s + t)
6+ 162 s
3t2u2(s + u)
6(t + u)
6(2(t + u)s
2
− 7(t2
+u2)s+ 5
(t3
+u3))H(3, 2, y)(s+ t)
6 − 9s2t2u2(t+u)
6(10 s
14+ (60t+ 74u)s
13+ 2(85t
2+ 94ut+ 129u
2)s12
+ 3(100t
3
+74ut2
+123u2t+190u
3)s11
+(360t
4+199u t
3+954u
2t2
+467u3t+900u
4)s10
+(300t
5−194ut4
+4854 u2t3
+635u3t2
+348u4t
+ 1074u5)s9
+ 2(85t
6 − 429u t5
+ 4734u2t4
+ 2414u3t3 − 498u
4t2
+ 135u5t+ 492u
6)s8
+(60t
7 − 874ut6
+ 8919u2t5
+ 5677u3t4
+ 1791u4t3 − 159u
5t2
+ 165u6t+ 678u
7)s7
+(10t
8 − 337ut7
+ 4848u2t6 − 2634 u
3t5
+ 4506u4t4
+ 5835u5t3
+ 288u6t2
+ 39u7t
+ 330u8)s6
+ u(− 36t
8+ 1746ut
7 − 7930u2t6
+ 1614u3t5
+ 14679u4t4
+ 3583u5t3 − 339u
6t2
+ 150u7t+ 100u
8)s5
+ u2(360t
8
=− 4417u t7 − 1014u
2t6
+ 13797u3t5
+ 8278u4t4 − 689u
5t3
+ 306u6t2
+ 172u7t + 14u
8)s4
+ tu3(− 708t
7 − 45ut6
+ 4974u2t5
+6885u3t4
+1171u4t3−108u
5t2
+489u6t+44u
7)s3
+3t2u4(120 t
6+114ut
5+580u
2t4
+562u3t3
+152u4t2
+117u5t+42u
6)s2
+ t3u5(− 36t
5 − 53ut4
+ 526u2t3
+ 402u3t2
+ 271u4t+ 104 u
5)s+ t
4u6(10t
4+ 40ut
3+ 72u
2t2
+ 49u3t+ 56 u
4))H(0, y)(s+ t)
2
+ 9s2t2u2(s + u)
6(t + u)
6(6 s
8+ (78t + 22u)s
7+(324t
2+ 202ut + 42u
2)s6
+ 3(230 t
3+ 202ut
2+ 186u
2t + 7u
3)s5
+(876t
4
+ 962ut3
+ 1710u2t2
+ 103u3t+ 58u
4)s4
+ 2t(345t
4+ 481ut
3+ 1194u
2t2
+ 38 u3t+ 122u
4)s3
+ 2t2(162t
4+ 303ut
3+ 855u
2t2
+ 38u3t+ 162u
4)s2
+ t3(78t
4+ 202ut
3+ 558u
2t2
+ 103u3t+ 244 u
4)s+ t
4(6t
4+ 22ut
3+ 42u
2t2
+ 21u3t+ 58 u
4))H(1, y)(s+ t)
2
– 21 –
=−3
2t2u2(s+ u)
(462(t+ u)
6s16
+ 6(533t
7+ 3647ut
6+ 11355u
2t5
+ 18041u3t4
+ 18041u4t3
+ 11355u5t2
+ 3647u6t+ 533u
7)s15
+6(t+u)2(1725 t
6+9572ut
5+26881u
2t4
+27580u3t3
+26881u4t2
+9572u5t+1725 u
6)s14
+(20814t
9+169590ut
8+698271u
2t7
+1572623u3t6
+2180718u4t5
+2180718u5t4
+1572623u6t3
+698271u7t2
+169590 u8t+20814u
9)s13
+(t+u)2(28872t
8+187896ut
7
+ 702435 u2t6
+ 1379212u3t5
+ 1402562u4t4
+ 1379212u5t3
+ 702435u6t2
+ 187896u7t+ 28872u
8)s12
+(28752t
11+ 247032u t
10
+ 1200159u2t9
+ 3905948u3t8
+ 7929314u4t7
+ 10661099u5t6
+ 10661099u6t5
+ 7929314u7t4
+ 3905948u8t3
+ 1200159u9t2
+ 247032 u10t + 28752u
11)s11
+ (t + u)2(20598t
10+ 137298u t
9+ 671079u
2t8
+ 2337710u3t7
+ 4295427u4t6
+ 4577312u5t5
+ 4295427 u6t4
+ 2337710u7t3
+ 671079u8t2
+ 137298u9t+ 20598u
10)s10
+(10230t
13+ 94398ut
12+ 670143u
2t11
+ 3176397u3t10
+ 9253014u4t9
+ 16795202u5t8
+ 21138216u6t7
+ 21138216u7t6
+ 16795202u8t5
+ 9253014u9t4
+ 3176397u10t3
+ 670143u11
t2
+ 94398u12t + 10230u
13)s9
+ (t + u)2(3174t
12+ 28308u t
11+ 353829u
2t10
+ 1598364u3t9
+ 3798910u4t8
+ 5149552u5t7
+ 4884942u6t6
+ 5149552u7t5
+ 3798910u8t4
+ 1598364u9t3
+ 353829 u10t2
+ 28308u11t + 3174u
12)s8
+(462t
15+ 7482u t
14
+ 190719u2t13
+ 1263290u3t12
+ 4354796u4t11
+ 9652847u5t10
+ 14817008u6t9
+ 17262724u7t8
+ 17262724u8t7
+ 14817008u9t6
+ 9652847u10t5
+ 4354796u11t4
+ 1263290u12t3
+ 190719u13
t2
+ 7482u14t + 462u
15)s7
+ tu(t + u)2(690t
12+ 52407u t
11
=+300320u2t10
+958425u3t9
+2341562u4t8
+3965828u5t7
+4535936u6t6
+3965828u7t5
+2341562u8t4
+958425u9t3
+300320 u10t2
+52407u11t+690u
12)s6
+t2u2(6786 t
13+57592ut
12+322024u
2t11
+1440278u3t10
+4550721u4t9
+9574691u5t8
+13690372u6t7
+ 13690372u7t6
+ 9574691u8t5
+ 4550721u9t4
+ 1440278u10t3
+ 322024u11t2
+ 57592u12t + 6786 u
13)s5
+ t3u3(t + u)
2(74t
10
+ 34768ut9
+ 270574u2t8
+ 947815u3t7
+ 1872940u4t6
+ 2304682u5t5
+ 1872940u6t4
+ 947815 u7t3
+ 270574u8t2
+ 34768u9t
+ 74u10)s4
+ t4u4(t+ u)
3(4432t
8+ 44590ut
7+ 177657u
2t6
+ 382429u3t5
+ 481348u4t4
+ 382429u5t3
+ 177657u6t2
+ 44590u7t
+4432u8)s3
+t5u5
(t+u)4(2948t
6+20395ut
5+53828u
2t4
+72306u3t3
+53828u4t2
+20395u5t+2948u
6)s2
+720t6u6(t+u)
7(2t
2
+3ut+2 u2)s+288t
7u7(t+u)
6(t2
+ut+u2))
(s+t)−9s2t2u2(s+u)
2(t+u)
6(10s
14+(74t+60u)s
13+2(129 t
2+94ut+85u
2)s12
+ 3(190t
3+ 123ut
2+ 74u
2t + 100 u
3)s11
+(900t
4+ 467ut
3+ 954u
2t2
+ 199u3t + 360 u
4)s10
+(1074t
5+ 348ut
4+ 635u
2t3
+ 4854u3t2 − 194u
4t + 300u
5)s9
+ 2(492t
6+ 135ut
5 − 498u2t4
+ 2414u3t3
+ 4734 u4t2 − 429u
5t + 85u
6)s8
+(678t
7+ 165ut
6
− 159u2t5
+ 1791 u3t4
+ 5677u4t3
+ 8919u5t2 − 874u
6t+ 60u
7)s7
+(330 t
8+ 39ut
7+ 288u
2t6
+ 5835u3t5
+ 4506u4t4 − 2634u
5t3
+4848u6t2−337u
7t+10u
8)s6
+ t(100t
8+150ut
7−339u2t6
+3583 u3t5
+14679u4t4
+1614u5t3−7930u
6t2
+1746u7t−36u
8)s5
+ t2(14t
8+172ut
7+306u
2t6−689u
3t5
+8278u4t4
+13797 u5t3−1014u
6t2−4417u
7t+360u
8)s4
+ t3u(44t
7+489u t
6−108u2t5
+1171u3t4
+6885u4t3
+4974u5t2−45u
6t−708 u
7)s3
+3t4u2(42t
6+117ut
5+152u
2t4
+562u3t3
+580 u4t2
+114u5t+120u
6)s2
= + t5u3(104t
5+ 271ut
4+ 402u
2t3
+ 526u3t2 − 53u
4t− 36u
5)s + t
6u4(56t
4+ 49ut
3+ 72 u
2t2
+ 40u3t + 10u
4))H(0, z)
− 9s2t2u2(2(3 t
6+ 60ut
5 − 78u2t4
+ 490u3t3 − 78u
4t2
+ 60u5t+ 3u
6)s16
+(72t
7+ 1289ut
6+ 414u
2t5
+ 8005u3t4
+ 7845u4t3
+126u5t2
+1129u6t+40u
7)s15
+6(60t
8+900ut
7+1076u
2t6
+4412u3t5
+9687u4t4
+3894u5t3
+558u6t2
+678u7t+23 u
8)s14
+(1024t
9+ 12954ut
8+ 24576u
2t7
+ 46761u3t6
+ 163314u4t5
+ 154677u5t4
+ 29274u6t3
+ 11781u7t2
+ 8316u8t + 331 u
9)s13
+(1874t
10+ 20222ut
9+ 53220u
2t8
+ 61201u3t7
+ 246846u4t6
+ 451965u5t5
+ 210152u6t4
+ 17091u7t3
+ 26370u8t2
+ 11421u9t
+ 638u10)s12
+ 3(780t
11+ 7249u t
10+ 25014u
2t9
+ 30013u3t8
+ 86909u4t7
+ 276042u5t6
+ 269826u6t5
+ 71475u7t4
+ 13798u8t3
+ 15298u9t2
+ 4109u10t + 359 u
11)s11
+(2042t
12+ 16125ut
11+ 76122u
2t10
+ 155760u3t9
+ 296460u4t8
+ 1068120u5t7
+ 1786074u6t6
+ 1133742 u7t5
+ 352110u8t4
+ 166875u9t3
+ 68808u10t2
+ 12114u11t + 1520 u
12)s10
+(1240t
13+ 7152ut
12
+58566u2t11
+232980 u3t10
+464512u4t9
+1090308u5t8
+2341921u6t7
+2520886u7t6
+1455108u8t5
+740077u9t4
+345463u10t3
+84624u11t2
+10790 u12t+1573u
13)s9
+3(168t
14+208ut
13+10592u
2t12
+73981u3t11
+192464u4t10
+350678u5t9
+731518u6t8
– 22 –
= + 1095507u7t7
+ 938868u8t6
+ 596751u9t5
+ 345880u10t4
+ 133260 u11t3
+ 25570u12t2
+ 2627u13t + 352u
14)s8
+(124 t
15
−1050ut14
+11760u2t13
+109681u3t12
+348969u4t11
+744780u5t10
+1812415u6t9
+3571941u7t8
+4045692u8t7
+2838503u9t6
+1635744u10t5
+818670u11t4
+274406u12t3
+50556u13t2
+4374u14t+403u
15)s7
+(14t
16−459 ut15
+4194u2t14
+16667u3t13
+ 21936u4t12
+ 169446u5t11
+ 1113116u6t10
+ 3298442u7t9
+ 4969926u8t8
+ 4145565u9t7
+ 2172862u10t6
+ 899067u11t5
+ 350974u12t4
+ 118004u13
t3
+ 24360u14t2
+ 1596u15t + 66u
16)s6
+ 3tu(− 20 t
15+ 510ut
14 − 2846u2t13 − 25726u
3t12
−36057u4t11
+137862 u5t10
+687022u6t9
+1363652u7t8
+1488125u8t7
+962136u9t6
+387285u10t5
+104624u11t4
+27898u12t3
+ 10766u13
t2
+ 2505u14t + 88u
15)s5
+ t2u2(276t
14 − 4915u t13 − 35832u
2t12 − 60573u
3t11
+ 131822u4t10
+ 839823u5t9
+ 1989780u6t8
+ 2753037u7t7
+ 2394378u8t6
+ 1355826u9t5
+ 497554 u10t4
+ 108936u11t3
+ 16362u12t2
+ 4782u13t+ 1056 u
14)s4
+ t3u3(− 820t
13 − 4665ut12 − 3330u
2t11
+ 50014u3t10
+ 234315u4t9
+ 583398u5t8
+ 954377u6t7
+ 1055745 u7t6
+ 809880u8t5
+ 443150u9t4
+ 168838u10t3
+ 40614u11
t2
+ 5192u12t + 196u
13)s3
+ 3t4u4(t + u)
2(92 t
10+ 476ut
9+ 2090u
2t8
+ 7269u3t7
+ 17036u4t6
+ 25733u5t5
+ 22780 u6t4
+ 14183u7t3
+ 6446u8t2
+ 2047u9t+ 352u
10)s2 − t5u5
(t+ u)3(60t
8+ 29ut
7 − 1449u2t6
−4932u3t5−8177u
4t4−6609 u
5t3−3504u
6t2−1214u
7t−264u
8)s+t
6u6(t+u)
6(14 t
4+90ut
3+126u
2t2
+89u3t+66u
4))H(1, z)
=− 9s2t2u2(2(6t
6+ 78ut
5 − 33u2t4
+ 550u3t3 − 33u
4t2
+ 78u5t + 6 u
6)s16
+(130t
7+ 1727ut
6+ 1824u
2t5
+ 10515u3t4
+ 10515 u4t3
+ 1824u5t2
+ 1727u6t + 130u
7)s15
+ 6(104t
8+ 1295u t
7+ 2603u
2t6
+ 7743u3t5
+ 14182u4t4
+ 7743u5t3
+ 2603u6t2
+ 1295 u7t + 104u
8)s14
+(1747t
9+ 20760ut
8+ 60177u
2t7
+ 138345 u3t6
+ 311235u4t5
+ 311235u5t4
+ 138345u6t3
+ 60177u7t2
+ 20760u8t + 1747u
9)s13
+(3218t
10+ 37773ut
9+ 146652u
2t8
+ 339358 u3t7
+ 769808u4t6
+ 1107894u5t5
+ 769808u6t4
+ 339358u7t3
+ 146652 u8t2
+ 37773u9t + 3218u
10)s12
+ 3(1403t
11+ 16697u t
10+ 82856u
2t9
+ 227499u3t8
+ 514057u4t7
+ 898468u5t6
+ 898468u6t5
+ 514057u7t4
+ 227499u8t3
+ 82856u9t2
+ 16697u10t + 1403 u
11)s11
+ 2(2050t
12
+ 24939ut11
+ 154530u2t10
+ 531155u3t9
+ 1271385u4t8
+ 2420490u5t7
+ 3112438u6t6
+ 2420490u7t5
+ 1271385u8t4
+ 531155u9t3
+ 154530u10t2
+ 24939 u11t+ 2050u
12)s10
+(2989t
13+ 37142ut
12+ 287298 u
2t11
+ 1240898u3t10
+ 3321201u4t9
+ 6609462u5t8
+ 9856850u6t7
+ 9856850u7t6
+ 6609462u8t5
+ 3321201u9t4
+ 1240898u10
t3
+ 287298u11t2
+ 37142u12t
+ 2989u13)s9
+ 3(514 t
14+ 6775ut
13+ 65664u
2t12
+ 346961u3t11
+ 1076100u4t10
+ 2314869u5t9
+ 3821756u6t8
+ 4598458u7t7
+ 3821756u8t6
+ 2314869u9t5
+ 1076100u10t4
+ 346961u11t3
+ 65664u12
t2
+ 6775u13t + 514u
14)s8
+(493t
15+ 8076ut
14
+ 98952 u2t13
+ 596673u3t12
+ 2146416u4t11
+ 5342982u5t10
+ 10174467 u6t9
+ 14554545u7t8
+ 14554545u8t7
+ 10174467u9t6
+ 5342982u10
t5
+ 2146416u11t4
+ 596673u12t3
+ 98952u13t2
+ 8076u14t + 493 u
15)s7
+(72t
16+ 2194ut
15+ 36630u
2t14
= + 227075u3t13
+ 910630u4t12
+ 2784993u5t11
+ 6611664u6t10
+ 11660494u7t9
+ 14240640u8t8
+ 11660494u9t7
+ 6611664u10t6
+ 2784993u11
t5
+ 910630u12t4
+ 227075u13t3
+ 36630u14t2
+ 2194u15t + 72 u
16)s6
+ 3tu(100t
15+ 3071ut
14+ 18464u
2t13
+ 80084u3t12
+ 323267u4t11
+ 1009711u5t10
+ 2219756u6t9
+ 3327843u7t8
+ 3327843u8t7
+ 2219756u9t6
+ 1009711u10
t5
+ 323267u11t4
+ 80084u12t3
+ 18464u13t2
+ 3071u14t + 100 u
15)s5
+ t2u2(1146t
14+ 7452ut
13+ 43332u
2t12
+ 256857u3t11
+ 1020516u4t10
+ 2637270u5t9
+ 4640688u6t8
+ 5609726u7t7
+ 4640688u8t6
+ 2637270u9t5
+ 1020516u10
t4
+ 256857u11t3
+ 43332u12t2
+ 7452u13t + 1146u
14)s4
+ t3u3(316t
13+ 7702ut
12+ 60600u
2t11
+ 260422u3t10
+ 721307u4t9
+ 1402338u5t8
+ 1962295u6t7
+ 1962295u7t6
+ 1402338u8t5
+ 721307u9t4
+ 260422u10t3
+ 60600u11t2
+ 7702 u12t + 316u
13)s3
+ 3t4u4(t + u)
2(382t
10+ 2457u t
9+ 8650u
2t8
+ 21232u3t7
+ 37622u4t6
+ 46842u5t5
+ 37622u6t4
+ 21232u7t3
+ 8650u8t2
+ 2457u9t + 382u
10)s2
+ t5u5
(t + u)3(300t
8+ 1544ut
7+ 4776u
2t6
+ 9573u3t5
+ 12690u4t4
+ 9573u5t3
+ 4776u6t2
+ 1544u7t + 300u
8)s + 3t
6u6(t + u)
6(24t
4+ 37ut
3+ 56u
2t2
+ 37u3t + 24u
4))H(2, y)
}/(27s
3t3u3(s + t)
6(s + u)
6(t + u)
6)
A(2)5;CF nf
=
{− 432s
2t2(s2 − ts + t
2)u3(s + u)
6(t + u)
6H(0, z)H(1, y) (s + t)
7 − 324s2t2u3(s + u)
6(t + u)
6(s2 − ts
= + t2
+ u2)H(1, y) H(1, z)(s + t)
7 − 108s2t2u3(s + u)
6(t + u)
6(s2 − ts + t
2 − 3 u2)H(1, 1, y)(s + t)
7
− 324s2t2u3(s + u)
6(t + u)
6(s2 − t s + t
2+ u
2)H(1, 2, y)(s + t)
7+ 108s
2t3u3(s + u)
6(t + u)
6(t2
+ u2)H(0, y)H(0, z)(s + t)
6
+ 432s2(s− t)t2u5
(s + u)6
(t + u)6H(0, y)H(1, z)(s + t)
6+ 432s
3t2u2(s + u)
6(t + u)
6(t3
+ s2u)H(0, z)H(2, y)(s + t)
6
– 23 –
=+108s3t2u2(s+u)
6(t+u)
6(3 u
3+s
2(4t+3u)
)H(1, z)H(2, y)(s+t)
6−432s3t2u2(s+u)
6(t+u)
7(t2−ut+u2
)H(1, z)H(3, y)(s+t)
6
−432s2t3u5
(s+u)6(t+u)
6H(0, 0, y)(s+ t)
6−432s2t5u3(s+u)
6(t+u)
6H(0, 0, z) (s+ t)
6−108s2t2u3(s+u)
6(t+u)
6(3t
3+3u
2t
+ 4su2)H(0, 1, z)(s + t)
6+ 108s
2t2u3(s + u)
6(t + u)
6(− 3t
3 − 3u2t + 4s u
2)H(0, 2, y)(s + t)
6+ 108s
2t2u3(s + u)
6(t + u)
6(t3
+ u2t− 4su
2)H(1, 0, y)(s+ t)
6+ 108s
2t2u3(s+ u)
6(t+ u)
6(4 s
3+ t
3+ tu
2)H(1, 0, z)(s+ t)
6+ 108s
2t2u3(s+ u)
6(t+ u)
6(3s
3
+ 3u2s− 4tu
2)H(1, 1, z)(s + t)
6+ 432s
3t2u2(s + u)
6(t + u)
6(u3
+ s2t)H(2, 0, y)(s + t)
6+ 108s
3t2u3(s + u)
6(t + u)
6(s2
− 3u2)H(2, 1, y)(s+ t)
6+ 324s
3t2u2(s+ u)
6(t+ u)
7(s2
+ t2
+ u2 − tu
)H(2, 2, y)(s+ t)
6 − 432s3t2u2
(s+ u)6(t+ u)
7(t2 − ut
+u2)H(3, 2, y)(s+ t)
6− 18s2t2u3
(s+u)6(t+u)
6(9(t+ 2u)s
4+ 9(3t
2+ 6ut+ 2u
2)s3
+(27t
3+ 72ut
2+ 12u
2t+ 16u
3)s2
+ t(9t
3
+ 54u t2
+ 12u2t+ 20u
3)s+ 2t
2u(9t
2+ 9ut+ 8u
2))
H(1, y)(s+ t)4 − 18s
2t3u3(t+ u)
6(18s
11+ 51(t+ 2u) s
10+(33t
2+ 360ut
+203u2)s9
+(−27t
3+498ut
2+705 u
2t+156u
3)s8
+(−39t
4+420ut
3+776u
2t2
+546u3t−63 u
4)s7−3
(4t
5−108ut4−91u
2t3
=−106u3t2
+21u4t+98 u
5)s6−3u
(−64t
5−9ut4
+98u2t3
+142u3t2
+236u4t+121u
5)s5−u
(−48t
6−44ut5
+174u2t4
+711u3t3
+1102 u4t2
+897u5t+240u
6)s4−u2
(−16t
6−100ut5
+333u2t4
+948u3t3
+1084u4t2
+558u5t+83u
6)s3−3u
3(−16 t
6+8ut
5
+ 124u2t4
+ 199u3t3
+ 182u4t2
+ 60u5t+ 4u
6)s2 − t u5
(52t
4+ 135ut
3+ 186u
2t2
+ 147u3t+ 24u
4)s− 2t
2u6(4t
3+ 9ut
2+ 13u
2t
+ 8u3))H(0, y)(s+ t)
3 − 12t3u3
(s+ u)(24tu
(3t
3+ 4ut
2+ 4u
2t+ 3u
3)s15 − 6(t+ u)
2(19t
4 − 7ut3
+ 86u2t2 − 7u
3t+ 19u
4)s14
−(528 t
7+2241ut
6+5905u
2t5
+10806u3t4
+10806u4t3
+5905u5t2
+2241 u6t+528u
7)s13−(t+u)
2(999t
6+3708ut
5+7757u
2t4
+13636u3t3
+7757u4t2
+3708u5t+999u
6)s12−
(945 t
9+6444ut
8+18478u
2t7
+38524u3t6
+60985u4t5
+60985u5t4
+38524 u6t3
+18478u7t2
+6444u8t+945u
9)s11− (t+u)
2(408 t
8+1419ut
7−737u2t6−1221u
3t5
+6934u4t4−1221u
5t3−737u
6t2
+1419u7t
+ 408u8)s10
+ 2(− 9t
11+ 1365ut
10+ 9543 u
2t9
+ 28308u3t8
+ 43963u4t7
+ 44166u5t6
+ 44166u6t5
+ 43963u7t4
+ 28308u8t3
+ 9543u9t2
+ 1365u10t− 9u
11)s9
+ (t + u)2(33t
10+ 3726ut
9+ 16908u
2t8
+ 31720u3t7
+ 24859u4t6
+ 8028 u5t5
+ 24859u6t4
+ 31720u7t3
+ 16908u8t2
+ 3726u9t + 33 u
10)s8
+(3t
13+ 2076ut
12+ 13514u
2t11
+ 34430u3t10
+ 33548u4t9 − 29287u
5t8
− 114020u6t7 − 114020u
7t6 − 29287u
8t5
+ 33548u9t4
+ 34430u10t3
+ 13514u11t2
+ 2076u12t + 3 u
13)s7
+ tu(t + u)2(615t
10
= + 2129ut9 − 2862u
2t8 − 27958 u
3t7 − 70915u
4t6 − 96406u
5t5 − 70915u
6t4 − 27958u
7t3 − 2862u
8t2
+ 2129u9t + 615u
10)s6
+tu(87t
13+151ut
12−4613 u2t11−33895u
3t10−117246u
4t9−252106u
5t8−365426u
6t7−365426u
7t6−252106u
8t5−117246u
9t4
−33895u10t3−4613 u
11t2
+151u12t+87u
13)s5− t2u2
(t+u)2(61 t
10+1421ut
9+9539u
2t8
+31118u3t7
+60284u4t6
+74918u5t5
+ 60284u6t4
+ 31118u7t3
+ 9539u8t2
+ 1421u9t+ 61u
10)s4 − t3u3
(t+u)3(119t
8+ 1631ut
7+ 6699u
2t6
+ 14006u3t5
+ 17750u4t4
+14006u5t3
+6699u6t2
+1631u7t+119u
8)s3−t4u4
(t+u)4(133t
6+842ut
5+1972u
2t4
+2532u3t3
+1972 u4t2
+842u5t+133u
6)s2
−6t5u5(t+u)
7(8t
2+9ut+8 u
2)s−6t
6u6(t+u)
6(t2
+ut+u2))
(s+ t)−18s2t3u3(s+u)
3(t+u)
6(18s
11+51(2t+u)s
10+(203t
2
+360 ut+33u2)s9
+3(52t
3+235ut
2+166u
2t−9u
3)s8
+(−63t
4+546ut
3+776u
2t2
+420u3t−39u
4)s7−3
(98t
5+21ut
4−106u2t3
− 91u3t2 − 108u
4t+ 4u
5)s6 − 3t
(121t
5+ 236ut
4+ 142u
2t3
+ 98u3t2 − 9u
4t− 64u
5)s5 − t
(240t
6+ 897ut
5+ 1102u
2t4
+ 711u3t3
+174u4t2−44u
5t−48 u
6)s4− t2
(83t
6+558ut
5+1084u
2t4
+948u3t3
+333u4t2−100u
5t−16u
6)s3−3t
3(4t
6+60ut
5+182u
2t4
+199 u3t3
+124u4t2
+8u5t−16u
6)s2−t5u
(24t
4+147u t
3+186u
2t2
+135u3t+52u
4)s−2t
6u2(8t
3+13ut
2+9 u
2t+4u
3))H(0, z)
= + 18s2t2u3(16t
2u(3t
2+ u t+ 3u
2)s16 − 4t
(t5 − 96ut
4 − 125u2t3 − 125u
3t2 − 96u
4t+ u
5)s15
+ 3(− 21t
7+ 376ut
6+ 969u
2t5
+ 1014u3t4
+ 1053 u4t3
+ 460u5t2
+ 15u6t + 6u
7)s14
+ 3(− 91t
8+ 434u t
7+ 2445u
2t6
+ 3548u3t5
+ 4121u4t4
+ 3594u5t3
+ 1259u6t2
+ 200u7t + 42u
8)s13
+(− 507t
9 − 228ut8
+ 8958u2t7
+ 21034u3t6
+ 29016u4t5
+ 37554u5t4
+ 27842u6t3
+ 10398u7t2
+ 2643u8t + 394 u
9)s12
+ 3(− 139t
10 − 658ut9
+ 1402u2t8
+ 7968u3t7
+ 14642u4t6
+ 25576u5t5
+ 31288u6t4
+ 20652u7t3
+ 8197u8t2
+ 2094u9t + 242u
10)s11
+(− 33t
11 − 1944ut10 − 2626 u
2t9
+ 15924u3t8
+ 52455u4t7
+ 115368u5t6
+ 193671u6t5
+ 189594u7t4
+ 109994u8t3
+ 41340u9t2
+ 9291u10t+ 870u
11)s10
+(229t
12 − 1206ut11 − 7826u
2t10
+ 2016u3t9
+ 60801u4t8
+ 168742u5t7
+ 312211u6t6
+ 377892u7t5
+ 285136u8t4
+ 142036u9t3
+ 47343u10t2
+ 9112u11t + 698u
12)s9
+ 3(69 t
13 − 396ut12 − 3542u
2t11 − 3876u
3t10
+ 19403u4t9
+ 74332u5t8
+ 145298u6t7
+ 193458u7t6
+ 172121u8t5
+ 103198u9t4
+ 43468u10t3
+ 12394u11t2
+ 2015u12t+ 122u
13)s8
+(81 t
14 − 1338ut13 − 9602u
2t12 − 15144u
3t11
+ 41583u4t10
+ 217006u5t9
+ 472374u6t8
+ 692016u7t7
+ 711667u8t6
+ 501642 u9t5
+ 246150u10t4
+ 85492u11t3
+ 19953u12t2
+ 2646u13
t + 114u14)s7
– 24 –
= +(12t
15− 936ut14− 5785u
2t13− 9734 u
3t12
+ 23766u4t11
+ 151768u5t10
+ 374411u6t9
+ 611526u7t8
+ 725603u8t7
+ 609872u9t6
+355422u10t5
+143724u11t4
+39635 u12t3
+7044u13t2
+696u14t+16u
15)s6
+3tu(−112t
14−711ut13−1428u
2t12
+2680u3t11
+24408u4t10
+73333u5t9
+137580u6t8
+184601u7t7
+179614u8t6
+124026u9t5
+59992u10t4
+19831u11t3
+4174u12t2
+496u13t
+28 u14)s5
+ t2u(−48t
14−380ut13−1422u
2t12−453 u
3t11
+19778u4t10
+90336u5t9
+213354u6t8
+330336u7t7
+360906u8t6
+281670u9t5
+156716u10t4
+61605u11t3
+16236 u12t2
+2470u13t+144u
14)s4
+t3u2(−16t
13−340 ut12−1209u
2t11
+1822u3t10
+23522u4t9
+76164u5t8
+142722 u6t7
+179964u7t6
+159444u8t5
+99732u9t4
+43795u10t3
+13194 u11t2
+2510u12t+232u
13)s3
− 3t4u3(t + u)
2(16 t
10+ 56ut
9 − 124u2t8 − 1147u
3t7 − 3208u
4t6 − 5170u
5t5 − 5528u
6t4 − 3835u
7t3 − 1676u
8t2 − 424u
9t
− 48u10)s2
+ t5u5(t+ u)
3(52t
7+ 321ut
6+ 921u
2t5
+ 1569u3t4
+ 1779u4t3
+ 1230u5t2
+ 484u6t+ 84u
7)s+ 2t
6u6(t+ u)
7(4t
2
+ 5ut+ 8 u2))H(1, z) + 18s
2t2u2(16t
2u2(3t
2+ ut+ 3 u
2)s16 − 4tu
(t5 − 96ut
4 − 125u2t3 − 125u
3t2 − 96u
4t+ u
5)s15
+ 6(3t
8
+ 9ut7
+ 242u2t6
+ 567u3t5
+ 582u4t4
+ 567u5t3
+ 242u6t2
+ 9u7t + 3u
8)s14
+ 3(42t
9+ 221u t
8+ 1445u
2t7
+ 4311u3t6
+ 5693u4t5
+ 5693u5t4
+ 4311u6t3
+ 1445 u7t2
+ 221u8t+ 42u
9)s13
+ 2(197t
10+ 1416ut
9+ 6153 u
2t8
+ 18148u3t7
+ 29594u4t6
+ 32160u5t5
+ 29594u6t4
+ 18148u7t3
+ 6153u8t2
+ 1416u9t + 197u
10)s12
+ 3(242t
11+ 2199 ut
10+ 9451u
2t9
+ 27134u3t8
= + 50612u4t7
+ 62634u5t6
+ 62634u6t5
+ 50612u7t4
+ 27134u8t3
+ 9451u9t2
+ 2199u10t + 242u
11)s11
+ 2(435t
12+ 4803ut
11
+ 23010u2t10
+ 69466u3t9
+ 145491u4t8
+ 210555u5t7
+ 230976u6t6
+ 210555u7t5
+ 145491u8t4
+ 69466u9t3
+ 23010u10t2
+4803u11t+435u
12)s10
+(698t
13+9301ut
12+51105u
2t11
+170974u3t10
+406704u4t9
+698997u5t8
+884941u6t7
+884941u7t6
+ 698997 u8t5
+ 406704u9t4
+ 170974u10t3
+ 51105u11t2
+ 9301u12t+ 698 u
13)s9
+ 6(61t
14+ 1018ut
13+ 6515u
2t12
+ 24975u3t11
+ 68497u4t10
+ 139578u5t9
+ 209143u6t8
+ 237090u7t7
+ 209143 u8t6
+ 139578u9t5
+ 68497u10t4
+ 24975u11t3
+ 6515u12
t2
+1018u13t+61u
14)s8
+(114t
15+2655ut
14+20511 u
2t13
+93946u3t12
+304122u4t11
+729081u5t10
+1284397u6t9
+1678662u7t8
+1678662u8t7
+1284397u9t6
+729081u10t5
+304122 u11t4
+93946u12t3
+20511u13t2
+2655u14t+114u
15)s7
+2(8t
16+348ut
15
+ 3558u2t14
+ 20893u3t13
+ 82679u4t12
+ 233298u5t11
+ 478228u6t10
+ 720901u7t9
+ 821694u8t8
+ 720901u9t7
+ 478228u10t6
+ 233298u11t5
+ 82679u12
t4
+ 20893u13t3
+ 3558u14t2
+ 348u15t + 8u
16)s6
+ 3tu(28t
15+ 496ut
14+ 4255u
2t13
+ 21403u3t12
= + 71760u4t11
+ 172018u5t10
+ 302499u6t9
+ 397333u7t8
+ 397333u8t7
+ 302499 u9t6
+ 172018u10t5
+ 71760u11t4
+ 21403u12t3
+4255u13t2
+496u14t+28u
15)s5
+2t2u2(72t
14+1235u t
13+8343u
2t12
+34020u3t11
+97435u4t10
+204801u5t9
+317982u6t8
+367512u7t7
+317982u8t6
+204801u9t5
+97435u10t4
+34020u11t3
+8343u12t2
+1235u13t+72u
14)s4
+t3u3(232t
13+2510ut
12
+ 13689u2t11
+ 49393u3t10
+ 127070 u4t9
+ 236640u5t8
+ 321522u6t7
+ 321522u7t6
+ 236640u8t5
+ 127070 u9t4
+ 49393u10t3
+ 13689u11t2
+ 2510u12t+ 232u
13)s3
+ 6t4u4(t+ u)
2(24t
10+ 212ut
9+ 892u
2t8
+ 2315u3t7
+ 4004u4t6
+ 4762u5t5
+ 4004u6t4
+2315u7t3
+892u8t2
+212u9t+24u
10)s2
+ t5u5(t+u)
3(84t
8+484ut
7+1347u
2t6
+2364u3t5
+2802u4t4
+2364u5t3
+1347u6t2
+ 484u7t + 84 u
8)s + 2t
6u6(t + u)
6(8t
4+ 13ut
3+ 18u
2t2
+ 13u3t + 8 u
4))H(2, y)
}/(27s
3t3u3(s + t)
6(s + u)
6(t + u)
6)
A(2)
5;n2f
= 2
{t3uH(2, y) + t
3uH(1, z)− tu
(t2
+ u2)H(0, y)− tu
(t2
+ u2)H(0, z) + tu
3H(2, y) + t u
3H(1, z)
+ s4
+ 2s3t + 2s
3u + 3s
2t2
+ 3s2u2
+ 2st3
+ 2su3
+ t4
+ 2t3u + 3t
2u2
+ 2tu3
+ u4
}/(3stu
)
A(2)
6;C2A
=
{3s
2t2(s+ t)
6u2(t+u)
2((
363t4
+ 492ut3
+ 504u2t2
+ 492 u3t+ 363u
4)s4
+ 2(363t
5+ 479ut
4− 58u2t3− 58u
3t2
+ 479 u4t
= + 363u5)s3
+ 9(t + u)2(121t
4 − 10ut3 − 134u
2t2 − 10u
3t + 121u
4)s2
+ 6(t + u)3(121t
4+ 35ut
3+ 12u
2t2
+ 35u3t + 121u
4)s
+363(t+u)4(t2
+ut+u2)2)
H(1, z) H(2, y)(s+u)6
+3s2t2(s+t)
2u2(t+u)
6(363s
8+726(3t+u)s
7+3
(2057t
2+796ut+363u
2)s6
+ 6(1815t
3+ 480ut
2+ 348u
2t+ 121u
3)s5
+(13068t
4+ 1782ut
3− 297u2t2
+ 958u3t+ 363 u
4)s4
+ 2t(5445t
4+ 891ut
3− 1296u2t2
−58u3t+246 u
4)s3
+ t2(6171t
4+2880ut
3−297u2t2−116u
3t+504 u
4)s2
+2t3(1089t
4+1194ut
3+1044u
2t2
+479u3t+246 u
4)s
+ 363t4(t2
+ ut+ u2)2)
H(0, 0, y)(s+ u)6
+ 36 s2t2(s+ t)
2u2(t+ u)
6(22s
8+ 44(3t+ u)s
7+ 2(187t
2+ 70u t+ 33u
2)s6
+(660t
3
+ 147ut2
+ 246u2t + 44u
3)s5
+(792t
4+ 41ut
3+ 360u
2t2
+ 115u3t + 22u
4)s4
+ t(660t
4+ 2ut
3+ 246u
2t2
+ 95u3t + 64u
4)s3
+ t2(374 t
4+ 54ut
3+ 84u
2t2
+ 9u3t+ 84u
4)s2
+ t3(132t
4+ 63u t
3+ 36u
2t2− 11u
3t+ 54u
4)s+ t
4(22t
4+ 21ut
3+ 18u
2t2
+ 4u3t
+ 18u4))H(0, z)H(0, 0, y)(s+ u)
6 − 36s2t2(s+ t)
2u2(t+ u)
6(22s
8+ 3(44t+ 7u)s
7+(374t
2+ 63ut+ 18u
2)s6
+(660t
3+ 54ut
2
+ 36u2t+ 4u
3)s5
+(792t
4+ 2u t
3+ 84u
2t2− 11u
3t+ 18u
4)s4
+ t(660t
4+ 41ut
3+ 246u
2t2
+ 9u3t+ 54u
4)s3
+ t2(374t
4+ 147ut
3
+ 360u2t2
+ 95u3t+ 84u
4)s2
+ t3(132t
4+ 140ut
3+ 246u
2t2
+ 115u3t+ 64 u
4)s+ 22t
4(t2
+ut+u2)2)
H(1, z)H(0, 0, y) (s+u)6
– 25 –
= + 108s2t2(s + t)
6u2(t + u)
6(2s
4+ 4(t + u)s
3+ 6
(t2
+ u2)s2
+ 4(t3
+ u3)s + 2t
4+ 2u
4 − 2tu3 − 3t
2u2
− 2t3u)H(0, 0, y)H(0, 0, z)(s+ u)
6+ 18s
2t2(s+ t)
6u2(t+ u)
2((
44t4
+ 296ut3
+ 486u2t2
+ 316u3t+ 58u
4)s4
+ 2(15t
5+ 247ut
4
+634u2t3
+646u3t2
+271u4t+27u
5)s3
+3 (t+u)2(5t
4+150ut
3+228u
2t2
+146u3t+15u
4)s2−2 (t+u)
3(2t
4−91ut3−90u
2t2
− 97u3t− 4u
4)s + (t + u)
4(11t
4+ 94ut
3+ 105u
2t2
+ 72u3t + 6u
4))H(3, y) H(0, 1, z)(s + u)
6 − 108s2t2(s + t)
6u2(t + u)
6(2s
4
+ 2(2t + u)s3
+ 3(2t
2+ u
2)s2
+ 2(2t
3+ u
3)s + 2
(t4 − 2ut
3+ 6 u
2t2
+ u4))H(0, 0, y)H(0, 1, z)(s + u)
6
= + 36s2t2(s + t)
6u2
(t + u)2(2(11t
4+ 32ut
3+ 42u
2t2
+ 27u3t + 9u
4)s4
+(44t
5+ 115ut
4+ 95u
2t3
+ 9u3t2 − 11u
4t
+ 4u5)s3
+ 6 (t + u)2(11t
4+ 19ut
3+ 11u
2t2
+ 3u4)s2
+ (t + u)3(44 t
4+ 8ut
3 − 9u2t2
+ 21u4)s + 22(t + u)
4(t2
+ u t
+ u2)2)
H(1, z)H(0, 2, y)(s+ u)6 − 108s
2t2(s+ t)
6u2
(t+ u)6(2s
4+ 2(t+ 2u)s
3+ 3(t2
+ 2u2)s2
+ 2(t3
+ 2 u3)s+ 2
(t4
+ 6u2t2
−2u3t+u
4))H(0, 0, z) H(0, 2, y)(s+u)
6+108s
2t2(s+t)
6u2(t+u)
6(−2(t−2u)s
3−3(t2−2u
2)s2−2
(t3−2u
3)s+12tu
(t2−u t
+u2))H(0, 1, z)H(0, 2, y)(s+u)
6+216s
2t2(s+t)
6u2
(t+u)6(s4
+2us3
+3u2s2
+2u3s+(t2
+u t+u2)2)
H(0, 1, z)H(0, 3, y)(s+u)6
+18s2t2(s+t)
3u2
(t+u)6(3s
7+(6u−9t)s
6+(−48t
2+12ut+15u
2)s5−(56t
3+6ut
2+63u
2t−12u
3)s4−t2
(7t
2+36u t+222u
2)s3
+ 3t(11t
4 − 14ut3 − 70u
2t2 − 8u
3t− 8 u
4)s2
+ t2(28t
4 − 24ut3 − 81u
2t2 − 24u
3t− 30u
4)s + t
3(8t
4 − 6ut3 − 15u
2t2 − 12u
3t
=− 14u4))H(0, z) H(1, 0, y)(s+u)
6− 18s2t2(s+ t)
3u2(t+u)
6(8s
7+ (28t− 6u)s
6+ 3
(11t
2− 8ut− 5u2)s5−
(7t
3+ 42ut
2+ 81u
2t
+12 u3)s4−2
(28t
4+18ut
3+105u
2t2
+12u3t+7u
4)s3−6t
(8t
4+ut
3+37u
2t2
+4u3t+5u
4)s2−3
(3 t
6−4ut5
+21u2t4
+8u4t2)s
+3t4(t3
+2ut2
+5u2t+4 u
3))H(1, z)H(1, 0, y)(s+u)
6+108s
2t2(s+t)
6u2(t+u)
6(2s
4+2(2t+u)s
3+3(2t
2+u
2)s2
+2(2 t
3+u
3)s
+ 2t4
+ 2u4− 2tu
3+ 9t
2u2− 6t
3u)H(0, 1, z) H(1, 0, y)(s+u)
6− 18s2t2(s+ t)
6u2(t+u)
3(2t(7t
2+ 15u t+ 12u
2)s4
+ 12(t4
+ 2ut3
+2u2t2−u4
)s3
+3(t+u)2(5t
3+17ut
2+31u
2t−5u
3)s2
+6(t+u)3(t3
+ut2
+u2t−u3
)s− (t+u)
3(8t
4+4ut
3−3u2t2−18u
3t
+ 3 u4))H(3, y)H(1, 0, z)(s+u)
6− 108s2t2(s+ t)
6u2(t+u)
6(2s
4+ 4(t−u)s
3+ 6(t2
+ 2u2)s2
+ 4t3s+ 2t
4+ 2u
4+ 2t u
3+ 3t
2u2
+2t3u)H(0, 0, y)H(1, 0, z)(s+u)
6−216s3t2(s+ t)
6u2(t+u)
6(2(t−2u)s
2+3(t2
+u2)s+2
(t3−u3
))H(0, 2, y)H(1, 0, z)(s+u)
6
+ 108s2t2(s+ t)
6u2(t+ u)
6(2s
4+ 2(t+ 3u)s
3+ 3
(t2 − u2
)s2
+ 2(t3
+ 5u3)s+ 2
(t2
+ ut+ u2)2)
H(0, 3, y) H(1, 0, z)(s+ u)6
= + 108s2t2(s + t)
6u2(t + u)
6(2s
4+ (4t− 6u) s
3+(6t
2+ 9u
2)s2
+(4t
3 − 2u3)s + 2t
4+ 2u
4+ 2t u
3+ 3t
2u2
+ 2t3u)H(1, 0, y)H(1, 0, z)(s+u)
6+ 3s
2t2(s+ t)
6u2
(t+u)2((
363t4
+ 492ut3
+ 504u2t2
+ 492u3t+ 363u
4)s4
+ 2(363t
5+ 479ut
4
−58u2t3−58u
3t2
+479u4t+363u
5)s3
+9(t+u)2(121t
4−10ut3−134u
2t2−10u
3t+121u
4)s2
+6(t+u)3(121t
4+35ut
3+12u
2t2
+ 35u3t+ 121u
4)s+ 363(t+ u)
4(t2
+ ut+ u2)2)
H(1, 1, z)(s+ u)6
+ 36s2t2
(s+ t)6u2(t+ u)
2(2(11t
4+ 32ut
3+ 42u
2t2
+ 27u3t
+ 9 u4)s4
+(44t
5+ 115ut
4+ 95u
2t3
+ 9u3t2−11u
4t+ 4 u
5)s3
+ 6(t+u)2(11t
4+ 19ut
3+ 11u
2t2
+ 3u4)s2
+ (t+u)3(44t
4+ 8ut
3
−9u2t2
+21u4)s+22(t+u)
4(t2
+ut+u2)2)
H(0, y)H(1, 1, z)(s+u)6−36s
2t2(s+t)
6u2(t+u)
2(2(20t
4+59ut
3+84u
2t2
+59u3t
+20u4)s4
+8(6t
5+13ut
4+13u
2t3
+13u3t2
+13u4t+6u
5)s3
+6 (t+u)2(14t
4+19ut
3+22u
2t2
+19u3t+14u
4)s2
+(t+u)3(65t
4
+ 8ut3 − 18u
2t2
+ 8u3t + 65u
4)s + 44(t + u)
4(t2
+ ut + u2)2)
H(3, y)H(1, 1, z)(s + u)6
+ 108s2t2
(s + t)6u2(t + u)
6(2s
4
+ (4t− 2u)s3
+(6t
2 − 3u2)s2
+(4t
3 − 2u3)s+ 2
(t2
+ ut+ u2)2)
H(0, 0, y) H(1, 1, z)(s+ u)6 − 108s
2t2(s+ t)
6u2(t+ u)
6(4s
4
+ (6t− 2u)s3
+ 9(t2
+ u2)s2
+ 6(t3 − u3
)s + 4
(t2
+ u t + u2)2)
H(0, 3, y)H(1, 1, z)(s + u)6
+ 216s2t2(s + t)
6u3
(t + u)6(2s
3
− 3us2
+ 4u2s + 6t
(t2 − ut + u
2))
H(0, 1, z)H(1, 2, y)(s + u)6 − 216s
2t2(s + t)
6u3(t + u)
6(6s
3 − 6u s2
+ 6u2s + t
(2t
2 − 3ut
=+4u2))H(1, 0, z)H(1, 2, y) (s+u)
6+36s
2t2(s+t)
6u2(t+u)
2(2(11t
4+32ut
3+42u
2t2
+27u3t+9u
4)s4
+(44t
5+115ut
4+95u
2t3
+9u3t2−11 u
4t+4u
5)s3
+6(t+u)2(11t
4+19ut
3+11u
2t2
+3 u4)s2
+(t+u)3(44t
4+8ut
3−9u2t2
+21u4)s+22 (t+u)
4(t2
+ut
+u2)2)
H(1, z)H(2, 0, y)(s+u)6− 108s
2t2(s+ t)
6u2(t+u)
6(2s
4− 4(t−u)s3
+ 6(2t
2+u
2)s2
+ 4u3s+ 2t
4+ 2u
4+ 2tu
3+ 3t
2u2
+ 2t3u)H(0, 0, z)H(2, 0, y) (s+ u)
6 − 108s2t2(s+ t)
6u2(t+ u)
6(4s
4+ 2(5t+ 2u)s
3+ 3
(t2
+ 2u2)s2
+ 2(7t
3+ 2u
3)s+ 4t
4+ 4u
4
+ 4t u3
+ 6t2u2
+ 4t3u)H(0, 1, z)H(2, 0, y)(s+u)
6 − 108s2t2(s+ t)
6u2(t+u)
6(4s
4+ 6ts
3+ 9(t2
+ 2u2)s2
+(6t
3+ 4 u
3)s+ 4t
4
+4u4
+6tu3
+9t2u2
+6t3u)H(1, 0, z)H(2, 0, y) (s+u)
6+3s
2t2(s+ t)
6u2(t+u)
2((
363t4
+492ut3
+504u2t2
+492u3t+363u
4)s4
+2(363t
5+479ut
4−58u2t3−58u
3t2
+479u4t+363u
5)s3
+9(t+u)2(121t
4−10ut3−134u
2t2−10u
3t+121u
4)s2
+6(t+u)3(121t
4
+ 35ut3
+ 12u2t2
+ 35u3t + 121u
4)s + 363(t + u)
4(t2
+ ut + u2)2)
H(2, 2, y)(s + u)6
+ 36s2t2(s + t)
6u2(t + u)
2(2(9t
4
+ 27u t3
+ 42u2t2
+ 32u3t + 11u
4)s4
+(4t
5 − 11ut4
+ 9u2t3
+ 95 u3t2
+ 115u4t + 44u
5)s3
+ 6(t + u)2(3t
4+ 11u
2t2
+ 19u3t + 11u
4)s2
+ (t + u)3(21t
4 − 9u2t2
+ 8u3t + 44u
4)s + 22(t + u)
4(t2
+ ut + u2)2)
H(0, z)H(2, 2, y)(s + u)6
+ 108 s2t2(s+ t)
6u2(t+ u)
6(2s
4 − 2(t− 2u)s3 − 3
(t2 − 2 u
2)s2 − 2
(t3 − 2u
3)s+ 2
(t2
+ u t+ u2)2)
H(0, 0, z)H(2, 2, y)(s+ u)6
– 26 –
= + 432s2t2(s + t)
6u2
(t + u)6(s4
+ 3(t2
+ u2)s2 −
(t3
+ u3)s +
(t2
+ ut + u2)2)
H(0, 1, z)H(2, 2, y)(s + u)6
− 108s2t2
(s+ t)6u2(t+ u)
6(4s
4 − 2(t+ 2u)s3
+ 3(5t
2+ 8u
2)s2
+ 2(t3 − 2u
3)s+ 4
(t2
+ ut+ u2)2)
H(1, 0, z) H(2, 2, y)(s+ u)6
+ 324s2t2(s + t)
6u2(t + u)
6(2s
4+ 2(t + u)s
3+ 3
(t2
+ u2)s2
+ 2(t3
+ u3)s + 2
(t2
+ u t + u2)2)
H(0, 1, z)H(2, 3, y)(s + u)6
=− 108s2t2(s + t)
6u2
(t + u)6(2s
4+ 2(t + u)s
3+ 3
(t2
+ u2)s2
+ 2(t3
+ u3)s + 2
(t2
+ ut + u2)2)
H(1, 0, z)H(2, 3, y) (s + u)6
− 18s2t2(s + t)
6u2(t + u)
3(2u(12t
2+ 15ut + 7 u
2)s4 − 12
(t4 − 2u
2t2 − 2u
3t− u4
)s3 − 3(t + u)
2(5t
3 − 31ut2 − 17u
2t
− 5u3)s2 − 6(t + u)
3(t3 − ut2 − u2
t− u3)s− (t + u)
3(3t
4 − 18ut3 − 3u
2t2
+ 4u3t + 8 u
4))H(1, z)H(3, 0, y)(s + u)
6
− 108s2t2(s + t)
6u2(t + u)
6(2s
4+ 2(t + u)s
3+ 3
(t2
+ u2)s2
+ 2(t3
+ u3)s + 2
(t2
+ ut + u2)2)
H(0, 1, z)H(3, 0, y)(s + u)6
− 108s2t2
(s + t)6u2(t + u)
6(2s
4+ 10(t + u)s
3 − 3(t2
+ u2)s2
+ 6(t3
+ u3)s + 2
(t2
+ ut + u2)2)
H(1, 0, z)H(3, 0, y) (s + u)6
− 216s2t2(s + t)
6u2(t + u)
6(2s
4+ 2ts
3+ 9t
2s2
+ 2(t2
+ ut + u2)2)
H(1, 1, z)H(3, 0, y)(s + u)6
=− 18s2t2
(s + t)6u2(t + u)
3(2t(7t
2+ 15ut + 12u
2)s4
+ 12(t4
+ 2ut3
+ 2u2t2 − u4
)s3
+ 3(t + u)2(5t
3+ 17ut
2+ 31 u
2t
− 5u3)s2
+ 6(t + u)3(t3
+ ut2
+ u2t− u3
)s− (t + u)
3(8t
4+ 4ut
3 − 3u2t2 − 18u
3t + 3u
4))H(0, z)H(3, 2, y) (s + u)
6
− 36s2t2(s + t)
6u2(t + u)
2(2(20t
4+ 59ut
3+ 84u
2t2
+ 59u3t + 20u
4)s4
+ 8(6t
5+ 13ut
4+ 13u
2t3
+ 13u3t2
+ 13u4t + 6u
5)s3
+ 6(t + u)2(14t
4+ 19ut
3+ 22u
2t2
+ 19 u3t + 14u
4)s2
+ (t + u)3(65t
4+ 8ut
3 − 18u2t2
+ 8u3t + 65 u
4)s + 44(t + u)
4(t2
+ ut
+ u2)2)
H(1, z)H(3, 2, y) (s+ u)6
+ 216s2t2(s+ t)
6u2(t+ u)
6(2s
4+ 2ts
3+ 9t
2s2
+ 2(t2
+ ut+ u2)2)
H(0, 1, z)H(3, 2, y)(s+ u)6
− 216s2t2
(s+ t)6u2(t+ u)
6(2s
4+ 4(t+ 2u)s
3 − 3(t2 − u2
)s2
+ 2(t3
+ 3u3)s+ 2
(t2
+ ut+ u2)2)
H(1, 0, z) H(3, 2, y)(s+ u)6
+ 18s2t2(s + t)
6u2(t + u)
2((
58t4
+ 340u t3
+ 540u2t2
+ 340u3t + 58u
4)s4
+ 2(21t
5+ 265ut
4+ 658u
2t3
+ 658u3t2
+ 265u4t
+ 21u5)s3
+ 6(t+ u)2(5t
4+ 86u t
3+ 138u
2t2
+ 86u3t+ 5u
4)s2
+ 2(t+ u)3(t4
+ 97ut3
+ 96 u2t2
+ 97u3t+ u
4)s+ 3(t+ u)
4(t4
+ 30ut3
+ 36u2t2
+ 30u3t+u
4))H(1, z)H(3, 3, y)(s+u)
6+ 216s
2t2(s+ t)
6u2(t+u)
6(4s
4+ (6t+ 4u)s
3+ 3(t2
+ 2u2)s2
+ 4(2 t
3
+ u3)s+ 4
(t2
+ ut+ u2)2)
H(0, 1, z)H(3, 3, y) (s+ u)6 − 216s
3t2(s+ t)
6u3(t+ u)
6(2s
2 − 3us+ 4u2)H(1, 0, z)H(3, 3, y)(s+ u)
6
+ 216s2t2(s + t)
6u2(t + u)
6(4s
4+ 2 (t + u)s
3+ 9
(t2
+ u2)s2
+ 4(t2
+ ut + u2)2)
H(1, 1, z)H(3, 3, y)(s + u)6
= + 216s2t2(s+ t)
6u2(t+ u)
6(s4
+ 2(t+ u) s3
+ 3(t2
+ u2)s2
+ 2(t3
+ u3)s+ t
4+ u
4+ 6t
2u2 − 2 t
3u)H(0, y)H(0, 0, 1, z)(s+ u)
6
+ 216s2t2(s+ t)
6u3(t+ u)
6(2s
3 − 3us2
+ 4u2s+ 6t
(t2 − ut+ u
2))H(1, y) H(0, 0, 1, z)(s+ u)
6+ 108s
2t2(s+ t)
6u2(t+ u)
6(6s
4
+2(4t+u) s3
+15u2s2
+2(6t
3−u3)s+6
(t2
+u t+u2)2)
H(2, y)H(0, 0, 1, z)(s+u)6
+432s2t2(s+ t)
6u2
(t+u)6(2s
4+2(t+u)s
3
+ 3(t2
+ u2)s2
+ 2(t3
+ u3)s+ 2
(t2
+ ut+ u2)2)
H(3, y)H(0, 0, 1, z) (s+ u)6 − 36s
2t2(s+ t)
2u2(t+ u)
6(22s
8+ 3(44t+ 7u) s
7
+(374t
2+ 63ut+ 18u
2)s6
+(660t
3+ 54ut
2+ 36u
2t+ 4 u
3)s5
+(792t
4+ 2ut
3+ 84u
2t2 − 11u
3t+ 18u
4)s4
+ t(660t
4+ 41ut
3
+ 246u2t2
+ 9u3t+ 54u
4)s3
+ t2(374 t
4+ 147ut
3+ 360u
2t2
+ 95u3t+ 84u
4)s2
+ t3(132t
4+ 140u t
3+ 246u
2t2
+ 115u3t+ 64u
4)s
+ 22t4(t2
+ u t + u2)2)
H(0, 0, 2, y)(s + u)6
+ 216s2t2(s + t)
6u2(t + u)
6(s4
+ 2ts3
+ 3(t2
+ 2u2)s2
+ 2(t3 − u3
)s + t
4+ u
4
− 2tu3
+ 6t2u2)H(0, z)H(0, 0, 2, y)(s + u)
6+ 108s
2t2
(s + t)6u2(t + u)
6(2s
4+ (4t− 2u)s
3+(6t
2 − 3u2)s2
+(4t
3 − 2u3)s
+ 2(t2
+ ut+ u2)2)
H(1, z) H(0, 0, 2, y)(s+ u)6 − 108s
2t2(s+ t)
6u2(t+ u)
6(4s
4+ 2(4t+ u) s
3+ 3(4t
2+ 5u
2)s2
+(8t
3 − 2u3)s
+ 4(t4 − u t3 + 6u
2t2 − u3
t + u4))H(1, z)H(0, 0, 3, y)(s + u)
6+ 108s
2t2
(s + t)6u2(t + u)
6(2s
4+ 2(2t + u)s
3+ 3
(2t
2+ u
2)s2
+ 2(2t
3+ u
3)s + 2t
4+ 2u
4+ 2tu
3+ 3t
2u2
+ 2t3u)H(0, z) H(0, 1, 0, y)(s + u)
6 − 108s2t2(s + t)
6u2(t + u)
6(2s
4+ 2(2t + u) s
3
+ 3(2t
2+ u
2)s2
+ 2(2t
3+ u
3)s+ 2t
4+ 2u
4+ 2t u
3+ 3t
2u2
+ 2t3u)H(1, z)H(0, 1, 0, y)(s+ u)
6+ 108s
2t2(s+ t)
6u2(t+ u)
6(2s
4
= + (4t− 6u)s3
+(6t
2+ 9u
2)s2
+(4 t
3 − 2u3)s + 2
(t4
+ u4))H(0, y)H(0, 1, 0, z) (s + u)
6 − 216s2t2(s + t)
6u3(t + u)
6(6s
3
− 6us2
+ 6u2s + t
(2t
2 − 3ut + 4u2))H(1, y)H(0, 1, 0, z)(s + u)
6 − 108s2t2
(s + t)6u2(t + u)
6(2s
4 − 2(2t + 5u)s3
+ 3(4t
2
+ 5u2)s2 − 10u
3s+ 2
(t2
+ ut+ u2)2)
H(2, y)H(0, 1, 0, z) (s+ u)6
+ 216s3t2(s+ t)
6u2(t+ u)
6(4(t+ u)s
2 − 3(t2
+ u2)s+ 2
(t3
+u3))H(3, y)H(0, 1, 0, z) (s+u)
6−36s2t2(s+ t)
6u2(t+u)
2(2(11t
4+32ut
3+42u
2t2
+27u3t+9u
4)s4
+(44t
5+115ut
4+95u
2t3
+ 9u3t2 − 11 u
4t+ 4u
5)s3
+ 6(t+ u)2(11t
4+ 19ut
3+ 11u
2t2
+ 3 u4)s2
+ (t+ u)3(44t
4+ 8ut
3 − 9u2t2
+ 21u4)s+ 22 (t+ u)
4(t2
+ ut + u2)2)
H(0, 1, 1, z)(s + u)6 − 108s
2t2
(s + t)6u2(t + u)
6(2s
4+ (4t− 2u)s
3+(6t
2 − 3u2)s2
+(4t
3 − 2u3)s + 2
(t2
+ ut
+u2)2)
H(0, y) H(0, 1, 1, z)(s+u)6
+ 216s2t2(s+ t)
6u2(t+u)
6(2s
4+ 2ts
3+ 9t
2s2
+ 2(t2
+ut+u2)2)
H(3, y)H(0, 1, 1, z)(s+u)6
– 27 –
=− 36s2t2
(s+ t)2u2(t+u)
6(22s
8+ 3(44t+ 7u)s
7+(374t
2+ 63ut+ 18 u
2)s6
+(660t
3+ 54ut
2+ 36u
2t+ 4u
3)s5
+(792 t
4+ 2ut
3
+ 84u2t2 − 11u
3t+ 18u
4)s4
+ t(660t
4+ 41u t
3+ 246u
2t2
+ 9u3t+ 54u
4)s3
+ t2(374t
4+ 147ut
3+ 360 u
2t2
+ 95u3t+ 84u
4)s2
+ t3(132t
4+ 140ut
3+ 246u
2t2
+ 115u3t+ 64u
4)s+ 22t
4(t2
+ ut+ u2)2)
H(0, 2, 0, y)(s+ u)6
+ 108s2t2(s+ t)
6u2(t+ u)
6(2s
4
+ 12us3
+ 8 u3s + 2t
4+ 2u
4+ 2tu
3+ 3t
2u2
+ 2t3u)H(0, z)H(0, 2, 0, y) (s + u)
6+ 108s
2t2(s + t)
6u2(t + u)
6(2s
4+ (4t− 2u)s
3
+(6 t
2 − 3u2)s2
+(4t
3 − 2u3)s + 2
(t2
+ u t + u2)2)
H(1, z)H(0, 2, 0, y)(s + u)6
+ 36s2t2(s + t)
6u2
(t + u)2(2(11t
4
+ 32ut3
+ 42u2t2
+ 27u3t + 9u
4)s4
+(44t
5+ 115ut
4+ 95u
2t3
+ 9u3t2 − 11u
4t + 4u
5)s3
+ 6 (t + u)2(11t
4+ 19ut
3
+ 11u2t2
+ 3u4)s2
+ (t + u)3(44 t
4+ 8ut
3 − 9u2t2
+ 21u4)s + 22(t + u)
4(t2
+ u t + u2)2)
H(0, 2, 2, y)(s + u)6
+ 108s2t2(s + t)
6u2(t + u)
6(2s
4+ 2ts
3+ 3
(t2
+ 4u2)s2
+ 2(t3 − 2u
3)s + 2
(t2
+ ut + u2)2)
H(0, z)H(0, 2, 2, y)(s + u)6
=−216s2t2
(s+t)6u2(t+u)
6(s4
+2(t−u)s3
+3(t2
+u2)s2
+2(t3−2u
3)s+t
4+u
4−4tu3
+9t2u2−4t
3u)H(1, z) H(0, 2, 3, y)(s+u)
6
− 216s2t2(s + t)
6u2(t + u)
6(2s
4+ 2(t + u)s
3+ 3
(t2
+ u2)s2
+ 2(t3
+ u3)s + 2
(t2
+ u t + u2)2)
H(1, z)H(0, 3, 0, y)(s + u)6
+ 108s2t2(s+ t)
6u2
(t+ u)6(2s
4+ 2(t+ 3u)s
3+ 3
(t2 − u2
)s2
+ 2(t3
+ 5 u3)s+ 2
(t2
+ ut+ u2)2)
H(0, z)H(0, 3, 2, y) (s+ u)6
− 108s2t2(s + t)
6u2(t + u)
6(4s
4+ (6t− 2u)s
3+ 9
(t2
+ u2)s2
+ 6(t3 − u3
)s + 4
(t2
+ u t + u2)2)
H(1, z)H(0, 3, 2, y)(s + u)6
−108s3t2(s+ t)
6u2
(t+u)6(2(t+u)s
2+3(t2−3u
2)s+2
(t3
+3 u3))H(1, z)H(0, 3, 3, y)(s+u)
6+36s
2t2(s+ t)
2u2(t+u)
6(44s
8
+ (264t + 65u)s7
+(748t
2+ 203ut + 84u
2)s6
+ 3(440t
3+ 67ut
2+ 94u
2t + 16u
3)s5
+(1584t
4+ 43u t
3+ 444u
2t2
+ 104u3t
+ 40u4)s4
+ t(1320t
4+ 43ut
3+ 492 u
2t2
+ 104u3t + 118u
4)s3
+ t2(748t
4+ 201ut
3+ 444u
2t2
+ 104u3t + 168u
4)s2
+ t3(264t
4+ 203ut
3+ 282u
2t2
+ 104 u3t + 118u
4)s + t
4(44t
4+ 65ut
3+ 84u
2t2
+ 48u3t + 40 u
4))H(1, 0, 0, y)(s + u)
6
= + 216s2t2(s + t)
6u2(t + u)
6(2 s
4+ 4ts
3+(6t
2+ 9u
2)s2
+ 2(2t
3+ u
3)s + 2
(t4
+ u4))H(0, z)H(1, 0, 0, y)(s + u)
6
− 216s2t2(s + t)
6u2(t + u)
6(2s
4+ 4ts
3+ 6t
2s2
+ 4t3s + 2t
4+ 2u
4+ 2tu
3+ 9t
2u2)H(1, z)H(1, 0, 0, y)(s + u)
6
+ 108s2t2(s + t)
6u2(t + u)
6(2 s
4+ 4(t + u)s
3+ 6
(t2
+ u2)s2
+ 4(t3
+ u3)s + 2t
4+ 2 u
4 − 2tu3 − 3t
2u2
− 2t3u)H(0, y)H(1, 0, 0, z)(s + u)
6 − 108s2t2
(s + t)6u2(t + u)
6(2s
4 − 4(t− u)s3
+ 6(2t
2+ u
2)s2
+ 4 u3s + 2t
4+ 2u
4
+ 2tu3
+ 3t2u2
+ 2t3u)H(2, y)H(1, 0, 0, z) (s + u)
6 − 108s2t2(s + t)
6u2(t + u)
6(2s
4+ 4ts
3+ 6t
2s2
+ 4t3s + 2t
4+ 2u
4
− 2tu3
+ 9t2u2 − 6t
3u)H(0, y)H(1, 0, 1, z)(s + u)
6+ 216 s
2t2(s + t)
6u3(t + u)
6(2s
3 − 3us2
+ 4u2s + 6t
(t2 − u t
+ u2))H(1, y)H(1, 0, 1, z)(s + u)
6 − 216s2t2(s + t)
6u2
(t + u)6(2(t + 2u)s
3 − 3t2s2
+(4t
3+ 6u
3)s− tu
(2 t
2+ 3ut
+ 2u2))H(2, y)H(1, 0, 1, z)(s+u)
6+ 216s
2t2(s+ t)
6u2(t+u)
6(2s
4+ 2ts
3+ 9t
2s2
+ 2(t2
+u t+u2)2)
H(3, y)H(1, 0, 1, z)(s+u)6
=− 18s2t2(s + t)
3u2
(t + u)6(8s
7+ (28t− 6u)s
6+ 3
(11t
2 − 8ut− 5u2)s5 −
(7t
3+ 42ut
2+ 81u
2t + 12u
3)s4 − 2
(28t
4+ 18u t
3
+ 105u2t2
+ 12u3t + 7u
4)s3 − 6t
(8t
4+ ut
3+ 37u
2t2
+ 4 u3t + 5u
4)s2 − 3
(3t
6 − 4ut5
+ 21u2t4
+ 8u4t2)s + 3 t
4(t3
+ 2ut2
+ 5u2t + 4u
3))H(1, 0, 2, y)(s + u)
6+ 108s
2t2(s + t)
6u2(t + u)
6(2s
4+ (4t + 6u)s
3+(6t
2 − 3u2)s2
+ 2(2t
3+ 5u
3)s + 2t
4
+ 2u4
+ 10tu3 − 3t
2u2
+ 6t3u)H(0, z)H(1, 0, 2, y)(s + u)
6 − 216s2t2(s + t)
6u3(t + u)
6(2 s
3 − 3us2
+ 4u2s + 6t
(t2 − ut
+u2))H(1, z)H(1, 0, 3, y) (s+u)
6 − 18s2t2(s+ t)
2u2(t+u)
6(3s
8+ 2(51t+u)s
7+(486 t
2+ 200ut+ 30u
2)s6
+ 6(179t
3+ 130ut
2
+ 96u2t + 7 u
3)s5
+ 2(687t
4+ 677ut
3+ 945u
2t2
+ 265u3t + 29u
4)s4
+ 2t(537t
4+ 677ut
3+ 1344u
2t2
+ 658u3t + 170u
4)s3
+ 2 t2(243t
4+ 390ut
3+ 945u
2t2
+ 658u3t + 270u
4)s2
+ 2t3(51t
4+ 100ut
3+ 288u
2t2
+ 265u3t + 170u
4)s + t
4(3 t
4+ 2ut
3
+ 30u2t2
+ 42u3t + 58u
4))H(1, 1, 0, y)(s + u)
6+ 216 s
3t2(s + t)
6u3(t + u)
6(4s
2 − 3us + 2u2)H(0, z)H(1, 1, 0, y) (s + u)
6
=− 216s2t3(s + t)
6u3(t + u)
6(4t
2 − 3ut + 2u2)H(1, z)H(1, 1, 0, y)(s + u)
6 − 216s2t2(s + t)
6u2(t + u)
6(s4
+ 2(t− u) s3
+ 3(t2
+ 2u2)s2
+ 2t3s +
(t2
+ ut + u2)2)
H(0, y)H(1, 1, 0, z)(s + u)6 − 216s
2t2(s + t)
6u3(t + u)
6(6s
3 − 6u s2
+ 6u2s + t
(2t
2 − 3ut
+ 4u2))H(1, y)H(1, 1, 0, z) (s+ u)
6 − 108s2t2(s+ t)
6u2(t+ u)
6(8s
4+ 4(2t+ u)s
3+ 12
(t2
+ 3u2)s2
+ 4(2t
3+ u
3)s+ 8t
4+ 8u
4
+ 14t u3
+ 21t2u2
+ 14t3u)H(2, y)H(1, 1, 0, z)(s + u)
6 − 216s2t2(s + t)
6u2(t + u)
6(2s
4+ 4(t + 2u)s
3 − 3(t2 − u2
)s2
+ 2(t3
+ 3u3)s+ 2
(t2
+ ut+ u2)2)
H(3, y) H(1, 1, 0, z)(s+ u)6 − 18s
2t2(s+ t)
3u2(t+ u)
6(8s
7+ (28t− 6u) s
6+ 3(11t
2 − 8ut− 5u2)s5
−(7t
3+ 42ut
2+ 81u
2t+ 12 u
3)s4− 2
(28t
4+ 18ut
3+ 105u
2t2
+ 12u3t+ 7u
4)s3− 6t
(8t
4+ut
3+ 37u
2t2
+ 4u3t+ 5u
4)s2− 3
(3 t
6
− 4ut5
+ 21u2t4
+ 8u4t2)s + 3t
4(t3
+ 2ut2
+ 5u2t + 4 u
3))H(1, 2, 0, y)(s + u)
6+ 108s
2t2(s + t)
6u2(t + u)
6(2 s
4+ (4t− 6u)s
3
+(6t
2+ 9u
2)s2
+(4t
3 − 2u3)s+ 2 t
4+ 2u
4+ 2tu
3+ 3t
2u2
+ 2t3u)H(0, z)H(1, 2, 0, y)(s+ u)
6+ 216s
2t2(s+ t)
6u3(t+ u)
6(2s
3
– 28 –
=− 3us2
+ 4u2s+ 6t
(t2 − u t+ u
2))H(1, z)H(1, 2, 3, y)(s+ u)
6 − 36s2t2(s+ t)
2u2(t+ u)
6(22s
8+ 3(44t+ 7u)s
7+(374t
2+ 63ut
+ 18u2)s6
+(660t
3+ 54ut
2+ 36u
2t + 4u
3)s5
+(792t
4+ 2u t
3+ 84u
2t2 − 11u
3t + 18u
4)s4
+ t(660t
4+ 41ut
3+ 246u
2t2
+ 9u3t + 54u
4)s3
+ t2(374t
4+ 147ut
3+ 360u
2t2
+ 95u3t + 84u
4)s2
+ t3(132t
4+ 140ut
3+ 246u
2t2
+ 115u3t + 64 u
4)s
+ 22t4(t2
+ ut + u2)2)
H(2, 0, 0, y)(s + u)6 − 108 s
2t2(s + t)
6u2(t + u)
6(2s
4+ 4(t− u)s
3+ 6
(t2
+ 2u2)s2
+ 4t3s + 2t
4
+ 2u4
+ 2tu3
+ 3t2u2
+ 2t3u)H(0, z)H(2, 0, 0, y) (s + u)
6+ 108s
2t2(s + t)
6u2(t + u)
6(2s
4+ (4t− 2u)s
3+(6 t
2 − 3u2)s2
+(4t
3 − 2u3)s + 2
(t2
+ u t + u2)2)
H(1, z)H(2, 0, 0, y)(s + u)6
+ 36s2t2(s + t)
6u2
(t + u)2(2(11t
4+ 32ut
3+ 42u
2t2
+ 27u3t
+ 9u4)s4
+(44t
5+ 115ut
4+ 95u
2t3
+ 9u3t2 − 11u
4t + 4u
5)s3
+ 6 (t + u)2(11t
4+ 19ut
3+ 11u
2t2
+ 3u4)s2
+ (t + u)3(44 t
4
+ 8ut3 − 9u
2t2
+ 21u4)s + 22(t + u)
4(t2
+ u t + u2)2)
H(2, 0, 2, y)(s + u)6 − 108s
2t2(s + t)
6u2(t + u)
6(2s
4+ 2(t + 4u)s
3
+ 3t2s2
+ 2(t3
+ 6u3)s + 2
(t4
+ u4))H(0, z)H(2, 0, 2, y)(s + u)
6 − 216s2t2(s + t)
6u2(t + u)
6(s4
+ (4t− 2u)s3
+ 3u2s2
+(6t
3 − 4u3)s +
(t2
+ ut + u2)2)
H(1, z)H(2, 0, 3, y)(s + u)6 − 108s
2t2
(s + t)6u2(t + u)
6(2s
4+ 2(2t + 5u)s
3+(6t
2
− 3u2)s2
+(4t
3+ 6u
3)s + 2t
4+ 2u
4+ 2tu
3+ 3t
2u2
+ 2t3u)H(0, z)H(2, 1, 0, y)(s + u)
6 − 216s2t2(s + t)
6u2(t + u)
6(2s
4
+ 2(2 t + u)s3
+ 3(2t
2+ u
2)s2
+ 2(2t
3+ u
3)s + 2t
4+ 2 u
4+ 2tu
3+ 3t
2u2
+ 2t3u)H(1, z)H(2, 1, 0, y)(s + u)
6
= + 36s2t2
(s + t)6u2(t + u)
2(2(11t
4+ 32ut
3+ 42u
2t2
+ 27u3t + 9 u
4)s4
+(44t
5+ 115ut
4+ 95u
2t3
+ 9u3t2 − 11u
4t
+ 4 u5)s3
+ 6(t + u)2(11t
4+ 19ut
3+ 11u
2t2
+ 3u4)s2
+ (t + u)3(44t
4+ 8ut
3 − 9u2t2
+ 21u4)s + 22(t + u)
4(t2
+ ut
+u2)2)
H(2, 2, 0, y)(s+u)6−216s
2t2(s+t)
6u2
(t+u)6(s4−2(t+u)s
3+6(t2
+u2)s2
+(t2
+u t+u2)2)
H(0, z)H(2, 2, 0, y)(s+u)6
+ 432s2t2(s + t)
6u2
(t + u)6(s4
+ 3(t2
+ u2)s2 −
(t3
+ u3)s +
(t2
+ ut + u2)2)
H(1, z)H(2, 2, 3, y)(s + u)6
− 108s2t2
(s + t)6u2(t + u)
6(2s
4+ 2(t + u)s
3+ 3
(t2
+ u2)s2
+ 2(t3
+ u3)s + 2
(t2
+ ut + u2)2)
H(1, z)H(2, 3, 0, y) (s + u)6
− 108s2t2(s + t)
6u2(t + u)
6(2s
4+ 2(t + u)s
3+ 3
(t2
+ u2)s2
+ 2(t3
+ u3)s + 2
(t2
+ u t + u2)2)
H(0, z)H(2, 3, 2, y)(s + u)6
+ 432s2t2(s + t)
6u2
(t + u)6(2s
4+ 2(t + u)s
3+ 3
(t2
+ u2)s2
+ 2(t3
+ u3)s + 2
(t2
+ ut + u2)2)
H(1, z)H(2, 3, 3, y) (s + u)6
− 18s2t2(s + t)
6u2(t + u)
3(2u(12t
2+ 15ut + 7 u
2)s4 − 12
(t4 − 2u
2t2 − 2u
3t− u4
)s3 − 3(t + u)
2(5t
3 − 31ut2 − 17u
2t
− 5u3)s2 − 6(t + u)
3(t3 − ut2 − u2
t− u3)s− (t + u)
3(3t
4 − 18ut3 − 3u
2t2
+ 4u3t + 8 u
4))H(3, 0, 2, y)(s + u)
6
=− 108s2t2(s + t)
6u2(t + u)
6(2 s
4+ 2(t− u)s
3+ 3
(t2
+ 3u2)s2
+ 2(t3 − 3u
3)s + 2
(t2
+ ut + u2)2)
H(0, z)H(3, 0, 2, y)(s + u)6
− 216s2t2
(s+ t)6u2(t+ u)
6(2s
4+ 2ts
3+ 9t
2s2
+ 2(t2
+ u t+ u2)2)
H(1, z)H(3, 0, 2, y)(s+ u)6 − 216s
3t2(s+ t)
6u3
(t+ u)6(2s
2
− 3us + 4u2)H(1, z)H(3, 0, 3, y)(s + u)
6 − 18s2t2
(s + t)6u2(t + u)
3(2u(12t
2+ 15ut + 7u
2)s4 − 12
(t4 − 2u
2t2 − 2u
3t
− u4)s3 − 3(t + u)
2(5t
3 − 31ut2 − 17 u
2t− 5u
3)s2 − 6(t + u)
3(t3 − ut2 − u2
t− u3)s− (t + u)
3(3t
4 − 18ut3 − 3u
2t2
+ 4u3t + 8u
4))H(3, 2, 0, y) (s + u)
6 − 108s2t2(s + t)
6u2(t + u)
6(2s
4+ 10(t + u)s
3 − 3(t2
+ u2)s2
+ 6(t3
+ u3)s + 2
(t2
+ u t
+u2)2)
H(0, z)H(3, 2, 0, y)(s+u)6−216s
2t2(s+ t)
6u2
(t+u)6(2s
4+2ts
3+9t
2s2
+2(t2
+ut+u2)2)
H(1, z)H(3, 2, 0, y)(s+u)6
− 36s2t2(s + t)
6u2(t + u)
2(2(20 t
4+ 59ut
3+ 84u
2t2
+ 59u3t + 20u
4)s4
+ 8(6t
5+ 13ut
4+ 13 u
2t3
+ 13u3t2
+ 13u4t + 6u
5)s3
+ 6(t + u)2(14t
4+ 19u t
3+ 22u
2t2
+ 19u3t + 14u
4)s2
+ (t + u)3(65t
4+ 8ut
3 − 18 u2t2
+ 8u3t + 65u
4)s + 44(t + u)
4(t2
+ ut
+ u2)2)
H(3, 2, 2, y)(s + u)6 − 216s
2t2(s + t)
6u2(t + u)
6(2s
4+ 2us
3+ 9u
2s2
+ 2(t2
+ ut + u2)2)
H(0, z)H(3, 2, 2, y)(s + u)6
=+216s2t2(s+ t)
6u2(t+u)
6(4s
4+2(t+u)s
3+9(t2
+u2)s2
+4(t2
+ut+u2)2)
H(1, z)H(3, 2, 3, y)(s+u)6−216s
3t3
(s+ t)6(2s
2
−3ts+4t2)u2(t+u)
6H(1, z)H(3, 3, 0, y) (s+u)
6+18s
2t2(s+t)
6u2(t+u)
2((
58t4
+340ut3
+540u2t2
+340u3t+58u
4)s4
+2(21t
5
+ 265ut4
+ 658u2t3
+ 658u3t2
+ 265u4t+ 21u
5)s3
+ 6(t+ u)2(5t
4+ 86ut
3+ 138u
2t2
+ 86u3t+ 5u
4)s2
+ 2(t+ u)3(t4
+ 97ut3
+ 96u2t2
+ 97u3t+ u
4)s+ 3(t+ u)
4(t4
+ 30ut3
+ 36u2t2
+ 30u3t+ u
4))H(3, 3, 2, y)(s+ u)
6 − 216s3t2(s+ t)
6u3(t+ u)
6(2s
2
− 3us + 4u2)H(0, z)H(3, 3, 2, y)(s + u)
6+ 216s
2t2(s + t)
6u2(t + u)
6(4s
4+ 2(t + u)s
3+ 9
(t2
+ u2)s2
+ 4(t2
+ u t
+ u2)2)
H(1, z)H(3, 3, 2, y)(s + u)6
+ 216s2t2(s + t)
6u2
(t + u)6(4s
4+ 6(t + u)s
3+ 3
(t2
+ u2)s2
+ 8(t3
+ u3)s + 4
(t2
+ ut
+ u2)2)
H(1, z)H(3, 3, 3, y) (s + u)6 − 324s
2t2(s + t)
6u3(t + u)
6(2s
3+ 3us
2+ 2u
2s− 4t
(t2 − ut + u
2))H(0, 0, 0, 1, z)(s + u)
6
– 29 –
= + 432s2t2(s + t)
6u2
(t + u)6(s4
+ (2t− u)s3
+ 3(t2
+ u2)s2
+ 2t3s + t
4+ u
4+ 3 t
2u2 − t3u
)H(0, 0, 1, 0, y)(s + u)
6
+ 432s2t2(s+ t)
6u3(t+u)
6(3s
3+ 2u
2s− 2t
3 − 3tu2)H(0, 0, 1, 0, z)(s+u)
6+ 108s
2t2
(s+ t)6u2(t+u)
6(2s
4+ (4t− 2u)s
3+(6t
2
−3u2)s2
+(4t
3−2u3)s+2
(t2
+ut+u2)2)
H(0, 0, 1, 1, z)(s+u)6
+108s2t2(s+ t)
6u2(t+u)
6(2s
4+(4t−2u) s
3+(6t
2−3u2)s2
+(4t
3 − 2u3)s+ 2
(t2
+u t+u2)2)
H(0, 0, 2, 2, y)(s+u)6 − 108s
2t2(s+ t)
6u2(t+u)
6(4s
4+ 2(4t+u)s
3+ 3(4t
2+ 5u
2)s2
+(8t
3
−2 u3)s+4
(t4−ut3 +6u
2t2−u3
t+u4))
H(0, 0, 3, 2, y)(s+u)6
+108s2t2(s+t)
6u2(t+u)
6(2s
4+4(t−u) s
3+6(t2−u2
)s2
+4(t3
−u3)s+ 2t
4+ 2u
4+ 18t u
3− 3t2u2
+ 18t3u)H(0, 1, 0, 1, z)(s+u)
6− 108s2t2(s+ t)
6u2
(t+u)6(2s
4+ 2(2t+u)s
3+ 3(2t
2+u
2)s2
+ 2(2 t
3+ u
3)s+ 2t
4+ 2u
4+ 2tu
3+ 3t
2u2
+ 2t3u)H(0, 1, 0, 2, y) (s+ u)
6+ 432s
2t2(s+ t)
6u2(t+ u)
6(2s
4+ 2(2t+ u)s
3+ 3(2 t
2
+ u2)s2
+ 2(2t
3+ u
3)s+ 2t
4+ 2u
4+ 2tu
3+ 3t
2u2
+ 2t3u)H(0, 1, 1, 0, y)(s+ u)
6+ 108s
2t2(s+ t)
6u2(t+ u)
6(2s
4+ 4(t− u)s
3
+ 6(t2
+ 2u2)s2
+ 4t3s+ 2t
4+ 2u
4 − 10 tu3
+ 3t2u2 − 6t
3u)H(0, 1, 1, 0, z)(s+u)
6 − 108s2t2(s+ t)
6u2
(t+u)6(2s
4+ 2(2t+u)s
3
+ 3(2t
2+ u
2)s2
+ 2(2 t
3+ u
3)s + 2t
4+ 2u
4+ 2tu
3+ 3t
2u2
+ 2t3u)H(0, 1, 2, 0, y) (s + u)
6+ 108s
2t2(s + t)
6u2(t + u)
6(2s
4
+ (4t− 2u)s3
+(6 t
2 − 3u2)s2
+(4t
3 − 2u3)s + 2
(t2
+ u t + u2)2)
H(0, 2, 0, 2, y)(s + u)6 − 216s
2t2(s + t)
6u2(t + u)
6(s4
+ 2(t− 2u)s3
+ 3(t2
+ u2)s2
+ 2(t3 − u3
)s + t
4+ u
4+ 4tu
3+ 6t
3u)H(0, 2, 1, 0, y)(s + u)
6+ 108s
2t2(s + t)
6u2(t + u)
6(2s
4
= + (4t− 2u)s3
+(6t
2 − 3u2)s2
+(4 t
3 − 2u3)s + 2
(t2
+ ut + u2)2)
H(0, 2, 2, 0, y) (s + u)6 − 216s
2t2(s + t)
6u2(t + u)
6(s4
+2(t−u)s3
+3(t2
+u2)s2
+2(t3−2u
3)s+ t
4+u
4−4tu3
+9t2u2−4t
3u)H(0, 2, 3, 2, y)(s+u)
6−216s2t2(s+ t)
6u2(t+u)
6(2s
4
+ 2(t+u)s3
+ 3(t2
+u2)s2
+ 2(t3
+u3)s+ 2
(t2
+ut+u2)2)
H(0, 3, 0, 2, y)(s+u)6− 216s
2t2
(s+ t)6u2(t+u)
6(2s
4+ 2(t+u)s
3
+ 3(t2
+ u2)s2
+ 2(t3
+ u3)s+ 2
(t2
+ ut+ u2)2)
H(0, 3, 2, 0, y) (s+ u)6 − 108s
2t2(s+ t)
6u2(t+ u)
6(4s
4+ (6t− 2u)s
3+ 9
(t2
+ u2)s2
+ 6(t3 − u3
)s+ 4
(t2
+ u t+ u2)2)
H(0, 3, 2, 2, y)(s+ u)6 − 108s
3t2(s+ t)
6u2(t+ u)
6(2(t+ u)s
2+ 3(t2 − 3u
2)s+ 2
(t3
+3u3))
H(0, 3, 3, 2, y)(s+u)6
+108s2t2(s+t)
6u2(t+u)
6(2s
4+(4t−6u) s
3+3(2t
2+u
2)s2
+2(2t
3−5u3)s+2
(t4−2 ut
3+6u
2t2
+u4))H(1, 0, 0, 1, z)(s+u)
6−216s2t2(s+t)
6u2(t+u)
6(2s
4+4ts
3+6t
2s2
+4t3s+2t
4+2u
4+2tu
3+9t
2u2)H(1, 0, 0, 2, y)(s+u)
6
+ 216s2t2(s + t)
6u2(t + u)
6(4 s
4+ 8ts
3+ 3
(4t
2+ 3u
2)s2
+ 2(4t
3+ u
3)s + 4 t
4+ 4u
4+ 2tu
3+ 9t
2u2)H(1, 0, 1, 0, y)(s + u)
6
= + 108s2t2(s + t)
6u2(t + u)
6(2s
4+ 2(2t + 9u)s
3+(6t
2 − 3u2)s2
+ 2(2t
3+ 9u
3)s + 2
(t4 − 2ut
3 − 3u2t2 − 2u
3t
+u4))H(1, 0, 1, 0, z)(s+u)
6−216s2t2(s+t)
6u2(t+u)
6(2s
4+4ts
3+6t
2s2
+4t3s+2t
4+2u
4+2tu
3+9t
2u2)H(1, 0, 2, 0, y)(s+u)
6
− 216s2t2(s+ t)
6u3(t+u)
6(2s
3 − 3us2
+ 4 u2s+ 6t
(t2 −ut+u
2))H(1, 0, 3, 2, y)(s+u)
6+ 216s
2t2
(s+ t)6u2(t+u)
6(4s
4+ 8ts
3
+ 3(4t
2+ 3u
2)s2
+ 2(4t
3+u
3)s+ 4t
4+ 4u
4+ 2tu
3+ 9t
2u2)H(1, 1, 0, 0, y) (s+u)
6+ 108s
2t2(s+ t)
6u2(t+u)
6(2s
4+ 4(t+u)s
3
+ 6(t2
+ u2)s2
+ 4(t3
+ u3)s + 2t
4+ 2u
4 − 2tu3 − 3t
2u2 − 2t
3u)H(1, 1, 0, 0, z)(s + u)
6 − 432s2t2(s + t)
6u3(t + u)
6(2s
3
+ 3u2s− 3t
3 − 2tu2)H(1, 1, 0, 1, z)(s + u)
6 − 216s2t3
(s + t)6u3(t + u)
6(4t
2 − 3ut + 2u2)H(1, 1, 0, 2, y)(s + u)
6
+216 s2t2(s+t)
6u2(t+u)
6(4s
4+8(t+u)s
3+3(4t
2+u
2)s2
+(8t
3+6u
3)s+4t
4+4u
4+6tu
3+3t
2u2
+8t3u)H(1, 1, 1, 0, y)(s+u)
6
+ 324s2t2(s+ t)
6u3(t+u)
6(4s
3− 4us2
+ 4 u2s− t
(2t
2+ 3ut+ 2u
2))H(1, 1, 1, 0, z)(s+u)
6− 216s2t3(s+ t)
6u3(t+u)
6(4t
2− 3ut
+2u2)H(1, 1, 2, 0, y) (s+u)
6−216s2t2(s+t)
6u2(t+u)
6(2s
4+4ts
3+6t
2s2
+4t3s+2t
4+2u
4+2tu
3+9t
2u2)H(1, 2, 0, 0, y)(s+u)
6
=− 216s3t2
(s + t)6u3(t + u)
6(4s
2 − 3us + 2u2)H(1, 2, 1, 0, y)(s + u)
6+ 216 s
2t2(s + t)
6u3(t + u)
6(2s
3 − 3us2
+ 4u2s + 6t
(t2
− u t + u2))H(1, 2, 3, 2, y)(s + u)
6+ 108s
2t2(s + t)
6u2(t + u)
6(2s
4+ (4t− 2u)s
3+(6t
2 − 3u2)s2
+(4t
3 − 2 u3)s + 2
(t2
+ ut + u2)2)
H(2, 0, 0, 2, y)(s + u)6 − 216 s
2t2(s + t)
6u2(t + u)
6(s4 − 4(t + u)s
3+ 3
(3t
2+ u
2)s2 − 2
(2t
3+ u
3)s +
(t2
+ ut + u2)2)
H(2, 0, 1, 0, y)(s + u)6
+ 108s2t2(s + t)
6u2(t + u)
6(2s
4+ (4t− 2u) s
3+(6t
2 − 3u2)s2
+(4t
3 − 2u3)s + 2
(t2
+ u t + u2)2)
H(2, 0, 2, 0, y)(s + u)6 − 216s
2t2(s + t)
6u2(t + u)
6(s4
+ (4t− 2u)s3
+ 3u2s2
+(6t
3 − 4u3)s +
(t2
+ u t
+u2)2)
H(2, 0, 3, 2, y)(s+u)6− 108s
2t2(s+ t)
6u2(t+u)
6(4s
4+ (8t− 6u)s
3+ 3(4t
2+ 3u
2)s2
+(8t
3− 2 u3)s+ 4t
4+ 4u
4+ 6tu
3
+9t2u2
+6t3u)H(2, 1, 0, 0, y) (s+u)
6−216s2t2(s+t)
6u2(t+u)
6(2s
4+2(2t+u)s
3+3(2 t
2+u
2)s2
+2(2t
3+u
3)s+2t
4+2u
4+2tu
3
+3t2u2
+2t3u)H(2, 1, 0, 2, y)(s+u)
6−108s2t2(s+ t)
6u3(t+u)
6(6s
3−9us2
+2u2s+ t
(2t
2+3ut+2u
2))
H(2, 1, 1, 0, y)(s+u)6
−216s2t2(s+t)
6u2(t+u)
6(2s
4+2(2t+u) s
3+3(2t
2+u
2)s2
+2(2t
3+u
3)s+2t
4+2u
4+2t u
3+3t
2u2
+2t3u)H(2, 1, 2, 0, y)(s+u)
6
+ 108s2t2(s + t)
6u2
(t + u)6(2s
4+ (4t− 2u)s
3+(6t
2 − 3u2)s2
+(4t
3 − 2 u3)s + 2
(t2
+ ut + u2)2)
H(2, 2, 0, 0, y)(s + u)6
– 30 –
=− 108 s2t2(s + t)
6u2(t + u)
6(4s
4 − 2(2t + u)s3
+ 3(8t
2+ 5 u
2)s2
+(2u
3 − 4t3)s + 4
(t2
+ u t + u2)2)
H(2, 2, 1, 0, y)(s + u)6
+432s2t2(s+t)
6u2(t+u)
6(s4
+3(t2
+u2)s2−(t3
+u3)s+(t2
+u t+u2)2)
H(2, 2, 3, 2, y)(s+u)6−108s
2t2(s+t)
6u2(t+u)
6(2s
4
+ 2(t+u)s3
+ 3(t2
+u2)s2
+ 2(t3
+u3)s+ 2
(t2
+ut+u2)2)
H(2, 3, 0, 2, y)(s+u)6− 108s
2t2
(s+ t)6u2(t+u)
6(2s
4+ 2(t+u)s
3
+ 3(t2
+ u2)s2
+ 2(t3
+ u3)s+ 2
(t2
+ ut+ u2)2)
H(2, 3, 2, 0, y) (s+ u)6
+ 432s2t2(s+ t)
6u2(t+ u)
6(2s
4+ 2(t+ u)s
3+ 3
(t2
+ u2)s2
+ 2(t3
+ u3)s + 2
(t2
+ u t + u2)2)
H(2, 3, 3, 2, y)(s + u)6
+ 216s3t2(s + t)
6u2(t + u)
6((6t + 4u)s
2 − 3(2t
2+ u
2)s
+ 2(3 t
3+ u
3))H(3, 0, 1, 0, y)(s+ u)
6 − 216s2t2(s+ t)
6u2(t+ u)
6(2s
4+ 2ts
3+ 9t
2s2
+ 2(t2
+ ut+ u2)2)
H(3, 0, 2, 2, y)(s+ u)6
=− 216s3t2(s+ t)
6u3(t+ u)
6(2s
2 − 3us+ 4 u2)H(3, 0, 3, 2, y)(s+ u)
6 − 216s2t2(s+ t)
6u2(t+ u)
6(2 s
4+ 2ts
3+ 9t
2s2
+ 2(t2
+ ut
+ u2)2)
H(3, 2, 0, 2, y) (s + u)6 − 216s
3t2(s + t)
6u2(t + u)
6((6t + 4u)s
2 − 3(2 t
2+ u
2)s + 2
(3t
3+ u
3))H(3, 2, 1, 0, y)(s + u)
6
−216 s2t2(s+t)
6u2(t+u)
6(2s
4+2ts
3+9t
2s2
+2(t2
+u t+u2)2)
H(3, 2, 2, 0, y)(s+u)6
+216s2t2(s+t)
6u2(t+u)
6(4s
4+2(t+u)s
3
+ 9(t2
+ u2)s2
+ 4(t2
+ u t + u2)2)
H(3, 2, 3, 2, y)(s + u)6 − 216s
3t3(s + t)
6(2s
2 − 3 ts + 4t2)u2(t + u)
6H(3, 3, 0, 2, y)(s + u)
6
− 216s3t3(s+ t)
6(2s
2 − 3ts+ 4t2)u2(t+ u)
6H(3, 3, 2, 0, y)(s+ u)
6+ 216s
2t2
(s+ t)6u2(t+ u)
6(4s
4+ 2(t+ u)s
3+ 9(t2
+ u2)s2
+ 4(t2
+ ut+ u2)2)
H(3, 3, 2, 2, y)(s+ u)6
+ 216s2t2(s+ t)
6u2(t+ u)
6(4s
4+ 6(t+ u)s
3+ 3
(t2
+ u2)s2
+ 8(t3
+ u3)s+ 4
(t2
+ ut+ u2)2)
H(3, 3, 3, 2, y) (s+ u)6 − s2t2(s+ t)
3u2(t+ u)
3(7948(t+ u)
3s10
+(39359 t
4+ 155744ut
3+ 236082u
2t2
+ 155744u3t
+39359u4)s9
+(93651t
5+434331ut
4+850587u
2t3
+850587u3t2
+434331u4t+93651u
5)s8
+3(46598t
6+240304ut
5+550627u
2t4
+ 717154 u3t3
+ 550627u4t2
+ 240304u5t + 46598u
6)s7
+(139794 t
7+ 836962ut
6+ 2146599u
2t5
+ 3271156u3t4
+ 3271156u4t3
+ 2146599u5t2
+ 836962u6t+ 139794u
7)s6
+ 3(31217t
8+ 240304ut
7+ 715533 u
2t6
+ 1216094u3t5
+ 1422608u4t4
+ 1216094u5t3
+ 715533u6t2
+ 240304u7t + 31217u
8)s5
+(39359t
9+ 434331ut
8+ 1651881 u
2t7
+ 3271156u3t6
+ 4267824u4t5
+ 4267824u5t4
= + 3271156u6t3
+ 1651881u7t2
+ 434331u8t + 39359u
9)s4
+(7948 t
10+ 155744ut
9+ 850587u
2t8
+ 2151462u3t7
+ 3271156u4t6
+ 3648282 u5t5
+ 3271156u6t4
+ 2151462u7t3
+ 850587u8t2
+ 155744u9t + 7948 u
10)s3
+ 3tu(7948t
9+ 78694ut
8+ 283529u
2t7
+550627u3t6
+715533u4t5
+715533u5t4
+550627u6t3
+283529u7t2
+78694u8t+7948u
9)s2
+ t2u2(t+u)
2(23844t
6+108056ut
5
+ 194375 u2t4
+ 224106u3t3
+ 194375u4t2
+ 108056u5t + 23844u
6)s + t
3u3(t + u)
3(7948t
4+ 15515ut
3+ 23262u
2t2
+ 15515u3t
+ 7948 u4))
(s + u)3
+ 18s2t2u2((
11t6
+ 162ut5
+ 153 u2t4
+ 884u3t3
+ 255u4t2
+ 246u5t + 33u
6)s13
+(62 t
7+ 1339ut
6
+ 2160u2t5
+ 8525u3t4
+ 7390u4t3
+ 3807u5t2
+ 1728u6t + 189u
7)s12
+ 6(26t
8+ 774ut
7+ 1639u
2t6
+ 5548u3t5
+ 7678u4t4
+ 4900u5t3
+ 2621u6t2
+ 826u7t+ 84u
8)s11
+ 2(140t
9+ 4728ut
8+ 12480u
2t7
+ 37199u3t6
+ 69840u4t5
+ 60090u5t4
+ 36224u6t3
+ 17091u7t2
+ 4188u8t+ 404u
9)s10
+(534 t
10+ 13578ut
9+ 45012u
2t8
+ 119424u3t7
+ 270061u4t6
+ 311178u5t5
+ 220301u6t4
+ 125964u7t3
+ 47997u8t2
+ 9560u9t+ 839u
10)s9
+ 3(340t
11+ 5526ut
10+ 22370u
2t9
+ 55138u3t8
+ 129254u4t7
+ 190253u5t6
= + 166896u6t5
+ 109793u7t4
+ 53466u8t3
+ 15573u9t2
+ 2466u10t+ 189u
11)s8
+ 2(736t
12+ 9471u t
11+ 44292u
2t10
+ 110988u3t9
+ 235059u4t8
+ 387831u5t7
+ 413404 u6t6
+ 317445u7t5
+ 187035u8t4
+ 72214u9t3
+ 15774u10t2
+ 1827 u11t + 116u
12)s7
+ 2(708t
13+ 9054ut
12+ 47823u
2t11
+ 134712u3t10
+ 269098u4t9
+ 435561u5t8
+ 508839u6t7
+ 430834 u7t6
+ 288621u8t5
+ 141397u9t4
+ 43186u10t3
+ 7236u11t2
+ 541 u12t+ 22u
13)s6
+ 3t(285t
13+ 4132ut
12+ 24795u
2t11
+ 81510u3t10
+ 175113u4t9
+ 286188u5t8
+ 351323u6t7
+ 311558 u7t6
+ 211822u8t5
+ 112744u9t4
+ 42788u10t3
+ 10552u11t2
+ 1454 u12t + 56u
13)s5
+ t2(294t
13+ 5499ut
12+ 38730u
2t11
+ 148723u3t10
+ 362736u4t9
+ 642597u5t8
+ 864762u6t7
+ 853029 u7t6
+ 614934u8t5
+ 328490u9t4
+ 124788u10t3
+ 32430u11t2
+ 6072u12t+ 708u
13)s4
+ 2t3(22t
13+ 707u t
12+ 6399u
2t11
+ 29412u3t10
+ 82842u4t9
+ 162087u5t8
+ 239183 u6t7
+ 267073u7t6
+ 222465u8t5
+ 137118u9t4
+ 59592u10t3
+ 16485 u11t2
+ 2553u12t + 174u
13)s3
+6t4u(t+u)
2(26 t
10+335ut
9+1643u
2t8
+4383u3t7
+7465u4t6
+9430u5t5
+8350 u6t4
+5555u7t3
+2649u8t2
+809u9t+127u
10)s2
– 31 –
=+t5u2
(t+u)3(162t
8+1164ut
7+3573u
2t6
+6255u3t5
+7589u4t4
+5865 u5t3
+3192u6t2
+1112u7t+216u
8)s+t
6u3(t+u)
6(58 t
4
+ 100ut3
+ 153u2t2
+ 100u3t+ 58u
4))H(2, y)H(1, 0, z) (s+ u)
3+ st(s+ t)
2u2(t+ u)
2(1531t(t+ u)
4s13
+ 3(3029 t
6+ 15191ut
5
+ 28746u2t4
+ 30440u3t3
+ 14567u4t2
+ 3351u5t+ 120 u
6)s12
+(25433t
7+ 151345ut
6+ 347338u
2t5
+ 471508u3t4
+ 364546u4t3
+ 144937u5t2
+ 32273u6t + 1800u
7)s11
+(44445t
8+ 300713ut
7+ 814816u
2t6
+ 1300511u3t5
+ 1362455 u4t4
+ 833113u5t3
+ 303956u6t2
+ 65055u7t + 3960u
8)s10
+(53136t
9+ 409309ut
8+ 1281415u
2t7
+ 2291071u3t6
+ 2894942 u4t5
+ 2471851u5t4
+ 1320295u6t3
+ 459769u7t2
+ 87252u8t + 5040 u
9)s9
+(44445t
10+ 409309ut
9+ 1473770u
2t8
+ 2915618u3t7
+ 4102638u4t6
+ 4464012u5t5
+ 3318386u6t4
+ 1630106u7t3
+ 508285 u8t2
+ 77799u9t + 3960u
10)s8
+(25433t
11+ 300713u t
10+ 1281415u
2t9
+2915618u3t8
+4495118u4t7
+5664674u5t6
+5440250u6t5
+3552410u7t4
+1539427u8t3
+391013u9t2
+44585 u10t+1800u
11)s7
+(9087t
12+151345ut
11+814816u
2t10
+2291071u3t9
+4102638u4t8
+5664674u5t7
+6338504u6t6
+5147724u7t5
+2865079u8t4
+ 1027309u9t3
+ 196900u10t2
+ 15021 u11t + 360u
12)s6
+ t(1531t
12+ 45573ut
11+ 347338u
2t10
+ 1300511u3t9
+ 2894942u4t8
+4464012u5t7
+5440250u6t6
+5147724u7t5
+3498698u8t4
+1616591u9t3
+448090u10t2
+58725 u11t+2287u
12)s5
+t2u(6124t
11
+86238u t10
+471508u2t9
+1362455u3t8
+2471851u4t7
+3318386u5t6
+3552410u6t5
+2865079u7t4
+1616591u8t3
+581902u9t2
= + 110862 u10t+ 7726u
11)s4
+ t3u2(9186t
10+ 91320ut
9+ 364546 u
2t8
+ 833113u3t7
+ 1320295u4t6
+ 1630106u5t5
+ 1539427u6t4
+1027309u7t3
+448090u8t2
+110862u9t+11166u
10)s3
+t4u3(t+u)
2(6124t
7+31453ut
6+75907u
2t5
+120689u3t4
+142484 u4t3
+ 102628u5t2
+ 43273u6t+ 7726u
7)s2
+ t5u4(t+ u)
4(1531t
4+ 3929ut
3+ 7371u
2t2
+ 5873u3t+ 2287u
4)s+ 360t
6u6(t+ u)
4(t2
+ ut+ u2))H(0, y)(s+ u)
2+ st
2(s+ t)
2u (t+ u)
2(1531u(t+ u)
4s13
+ 3(120t
6+ 3351ut
5+ 14567u
2t4
+ 30440u3t3
+ 28746u4t2
+15191u5t+3029u
6)s12
+(1800t
7+32273ut
6+144937u
2t5
+364546u3t4
+471508u4t3
+347338u5t2
+151345u6t+25433u
7)s11
+(3960t
8+ 65055 ut
7+ 303956u
2t6
+ 833113u3t5
+ 1362455u4t4
+ 1300511u5t3
+ 814816 u6t2
+ 300713u7t + 44445u
8)s10
+(5040t
9+ 87252u t
8+ 459769u
2t7
+ 1320295u3t6
+ 2471851u4t5
+ 2894942u5t4
+ 2291071 u6t3
+ 1281415u7t2
+ 409309u8t
+ 53136u9)s9
+(3960 t
10+ 77799ut
9+ 508285u
2t8
+ 1630106u3t7
+ 3318386u4t6
+ 4464012 u5t5
+ 4102638u6t4
+ 2915618u7t3
= + 1473770u8t2
+ 409309u9t+ 44445 u
10)s8
+(1800t
11+ 44585ut
10+ 391013u
2t9
+ 1539427 u3t8
+ 3552410u4t7
+ 5440250u5t6
+ 5664674u6t5
+ 4495118u7t4
+ 2915618u8t3
+ 1281415u9t2
+ 300713u10t+ 25433u
11)s7
+(360t
12+ 15021ut
11+ 196900u
2t10
+ 1027309u3t9
+ 2865079u4t8
+ 5147724u5t7
+ 6338504u6t6
+ 5664674u7t5
+ 4102638 u8t4
+ 2291071u9t3
+ 814816u10t2
+ 151345u11t+ 9087u
12)s6
+ u(2287t
12+ 58725ut
11+ 448090u
2t10
+ 1616591u3t9
+ 3498698u4t8
+ 5147724u5t7
+ 5440250u6t6
+ 4464012u7t5
+ 2894942 u8t4
+ 1300511u9t3
+ 347338u10t2
+ 45573u11t+ 1531u
12)s5
+ tu2(7726t
11+ 110862ut
10+ 581902u
2t9
+1616591u3t8
+2865079u4t7
+3552410u5t6
+3318386u6t5
+2471851u7t4
+1362455 u8t3
+471508u9t2
+86238u10t+6124u
11)s4
+t2u3(11166t
10+110862ut
9+448090u
2t8
+1027309u3t7
+1539427u4t6
+1630106u5t5
+1320295u6t4
+833113u7t3
+364546u8t2
+ 91320u9t + 9186u
10)s3
+ t3u4(t + u)
2(7726t
7+ 43273ut
6+ 102628 u
2t5
+ 142484u3t4
+ 120689u4t3
+ 75907u5t2
+ 31453u6t
+ 6124 u7)s2
+ t4u5(t+u)
4(2287t
4+ 5873ut
3+ 7371u
2t2
+ 3929 u3t+ 1531u
4)s+ 360t
6u6(t+u)
4(t2
+ut+u2))
H(0, z)(s+u)2
=+3t2(s+t)
2u2(t+u)
(259(t+u)
5s14
+36(43 t
6+242ut
5+651u
2t4
+764u3t3
+651u4t2
+242u5t+43u
6)s13
+(4367t
7+26163ut
6
+ 84905u2t5
+ 124733u3t4
+ 124733u4t3
+ 84905u5t2
+ 26163u6t+ 4367u
7)s12
+ 4(1920t
8+ 12056 ut
7+ 43065u
2t6
+ 78684u3t5
+ 86470u4t4
+ 78684u5t3
+ 43065u6t2
+ 12056u7t+ 1920u
8)s11
+ 6(1534t
9+ 10415ut
8+ 38108 u
2t7
+ 83108u3t6
+ 101419u4t5
+ 101419u5t4
+ 83108u6t3
+ 38108u7t2
+ 10415u8t+ 1534u
9)s10
+ 12(640t
10+ 4992ut
9+ 18355 u
2t8
+ 44658u3t7
+ 62385u4t6
+ 60940u5t5
+ 62385u6t4
+ 44658u7t3
+ 18355u8t2
+ 4992u9t+ 640u
10)s9
+(4367t
11+ 41875u t
10+ 163877u
2t9
+ 417437u3t8
+ 677572u4t7
+ 645896u5t6
+ 645896 u6t5
+ 677572u7t4
+ 417437u8t3
+ 163877u9t2
+ 41875u10t + 4367 u
11)s8
+ 2(774t
12
+ 9924ut11
+ 46320u2t10
+ 124333 u3t9
+ 232260u4t8
+ 249279u5t7
+ 198284u6t6
+ 249279u7t5
+ 232260 u8t4
+ 124333u9t3
=+46320u10t2
+9924u11t+774u
12)s7
+(259t
13+5481ut
12+35278u
2t11
+110676u3t10
+240564 u4t9
+349066u5t8
+300068u6t7
+300068u7t6
+349066u8t5
+240564 u9t4
+110676u10t3
+35278u11t2
+5481u12t+259u
13)s6
+2tu(308t
12+3564ut
11+15365u
2t10
+42591u3t9
+94706u4t8
+136033u5t7
+141098u6t6
+136033u7t5
+94706u8t4
+42591u9t3
+15365u10t2
+3564u11t+308u
12)s5
+t2u2(426t
11+3380ut
10+15835u
2t9
+65921u3t8
+171209u4t7
+259557u5t6
+259557u6t5
+171209u7t4
+65921u8t3
+15835u9t2
+ 3380u10t+ 426u
11)s4 − 2t
3u3(t+ u)
2(34t
8 − 527u t7 − 6013u
2t6 − 19815u
3t5 − 26374u
4t4 − 19815u
5t3 − 6013u
6t2 − 527 u
7t
+ 34u8)s3
+ t4u4(t + u)
3(109t
6+ 2242ut
5+ 8867u
2t4
+ 13216u3t3
+ 8867u4t2
+ 2242u5t + 109u
6)s2
+ 30t5u5
(t + u)6(10t
2
+ 23ut + 10u2)s + 120t
6u6(t + u)
5(t2
+ u t + u2))H(0, y)H(0, z)(s + u)
2 − s2t(s + t)2u(t + u)
2((
360t6
+ 2287ut5
+ 7726u2t4
+ 11166u3t3
+ 7726u4t2
+ 2287 u5t+ 360u
6)s12
+ 9(200t
7+ 1669ut
6+ 6525u
2t5
+ 12318 u3t4
+ 12318u4t3
+ 6525u5t2
+ 1669u6t
+200u7)s11
+(3960t
8+44585ut
7+196900u
2t6
+448090u3t5
+581902u4t4
+448090u5t3
+196900u6t2
+44585u7t+3960u
8)s10
– 32 –
= +(5040t
9+ 77799ut
8+ 391013u
2t7
+ 1027309u3t6
+ 1616591u4t5
+ 1616591u5t4
+ 1027309u6t3
+ 391013u7t2
+ 77799u8t
+ 5040 u9)s9
+(3960t
10+ 87252ut
9+ 508285u
2t8
+ 1539427u3t7
+ 2865079u4t6
+ 3498698u5t5
+ 2865079u6t4
+ 1539427u7t3
+ 508285 u8t2
+ 87252u9t + 3960u
10)s8
+(1800t
11+ 65055u t
10+ 459769u
2t9
+ 1630106u3t8
+ 3552410u4t7
+ 5147724u5t6
+ 5147724u6t5
+ 3552410u7t4
+ 1630106u8t3
+ 459769u9t2
+ 65055 u10t + 1800u
11)s7
+(360t
12+ 32273ut
11+ 303956u
2t10
+1320295u3t9
+3318386u4t8
+5440250u5t7
+6338504u6t6
+5440250u7t5
+3318386u8t4
+1320295u9t3
+303956u10t2
+32273 u11t
+360u12)s6
+ tu(10053t
11+144937ut
10+833113 u
2t9
+2471851u3t8
+4464012u4t7
+5664674u5t6
+5664674u6t5
+4464012u7t4
+ 2471851u8t3
+ 833113u9t2
+ 144937u10t+ 10053 u
11)s5
+ tu(1531t
12+ 43701ut
11+ 364546u
2t10
+ 1362455u3t9
+ 2894942u4t8
+4102638u5t7
+4495118u6t6
+4102638u7t5
+2894942u8t4
+1362455u9t3
+364546u10t2
+43701 u11t+1531u
12)s4
+t2u2(6124t
11
+91320u t10
+471508u2t9
+1300511u3t8
+2291071u4t7
+2915618u5t6
+2915618u6t5
+2291071u7t4
+1300511u8t3
+471508u9t2
+91320 u10t+6124u
11)s3
+ t3u3(t+u)
2(9186t
8+67866u t
7+202420u
2t6
+342110u3t5
+394775u4t4
+342110u5t3
+202420u6t2
+ 67866u7t + 9186u
8)s2
+ t4u4(t + u)
3(6124t
6+ 27201u t
5+ 51370u
2t4
+ 58876u3t3
+ 51370u4t2
+ 27201u5t + 6124u
6)s
+ t5u5(t + u)
4(1531t
4+ 2963ut
3+ 4395u
2t2
+ 2963u3t + 1531 u
4))H(1, z)(s + u)
2 − s2t(s + t)2u(t + u)
2((
360 t6
+ 2287ut5
= + 7726u2t4
+ 11166u3t3
+ 7726u4t2
+ 2287u5t+ 360 u
6)s12
+ 9(200t
7+ 1669ut
6+ 6525u
2t5
+ 12318u3t4
+ 12318u4t3
+ 6525u5t2
+ 1669u6t+ 200u
7)s11
+(3960 t
8+ 44585ut
7+ 196900u
2t6
+ 448090u3t5
+ 581902u4t4
+ 448090u5t3
+ 196900u6t2
+ 44585u7t
+ 3960u8)s10
+(5040t
9+ 77799u t
8+ 391013u
2t7
+ 1027309u3t6
+ 1616591u4t5
+ 1616591u5t4
+ 1027309 u6t3
+ 391013u7t2
+ 77799u8t + 5040u
9)s9
+(3960 t
10+ 87252ut
9+ 508285u
2t8
+ 1539427u3t7
+ 2865079u4t6
+ 3498698 u5t5
+ 2865079u6t4
+ 1539427u7t3
+ 508285u8t2
+ 87252u9t + 3960 u
10)s8
+(1800t
11+ 65055ut
10+ 459769u
2t9
+ 1630106 u3t8
+ 3552410u4t7
+ 5147724u5t6
+ 5147724u6t5
+ 3552410u7t4
+ 1630106u8t3
+ 459769u9t2
+ 65055u10t + 1800u
11)s7
+(360t
12+ 32273ut
11
+ 303956u2t10
+ 1320295u3t9
+ 3318386u4t8
+ 5440250u5t7
+ 6338504u6t6
+ 5440250u7t5
+ 3318386 u8t4
+ 1320295u9t3
+ 303956u10t2
+ 32273u11t+ 360u
12)s6
+ tu(10053t
11+ 144937ut
10+ 833113u
2t9
+ 2471851u3t8
+ 4464012u4t7
+ 5664674u5t6
+ 5664674u6t5
+ 4464012u7t4
+ 2471851 u8t3
+ 833113u9t2
+ 144937u10t+ 10053u
11)s5
+ tu(1531t
12+ 43701ut
11+ 364546u
2t10
+ 1362455u3t9
+ 2894942 u4t8
+ 4102638u5t7
+ 4495118u6t6
+ 4102638u7t5
+ 2894942u8t4
+ 1362455u9t3
+ 364546u10t2
+ 43701u11t+ 1531u
12)s4
+ t2u2(6124t
11+ 91320ut
10+ 471508u
2t9
+ 1300511u3t8
+ 2291071u4t7
+ 2915618u5t6
+ 2915618u6t5
+ 2291071u7t4
+ 1300511 u8t3
+ 471508u9t2
+ 91320u10t + 6124u
11)s3
+ t3u3(t + u)
2(9186t
8+ 67866ut
7+ 202420u
2t6
+ 342110u3t5
+ 394775u4t4
+ 342110u5t3
+ 202420u6t2
+ 67866u7t+ 9186u
8)s2
+ t4u4
(t+ u)3(6124t
6+ 27201ut
5+ 51370u
2t4
+58876u3t3
+51370u4t2
+27201u5t+6124u
6)s+t
5u5(t+u)
4(1531t
4+2963u t
3+4395u
2t2
+2963u3t+1531u
4))H(2, y)(s+u)
2
=− 3s2t2
(t+u)2((
120t6
+ 300ut5
+ 109u2t4− 68u
3t3
+ 426u4t2
+ 616 u5t+ 259u
6)s14
+ 2(420t
7+ 1395ut
6+ 1339u
2t5
+ 425u3t4
+1903u4t3
+3872u5t2
+2870u6t+774u
7)s13
+(2640 t
8+11430ut
7+18489u
2t6
+14984u3t5
+19215u4t4
+37858u5t3
+40759u6t2
+ 21396u7t + 4367u
8)s12
+ 2(2460t
9+ 13545 ut
8+ 31286u
2t7
+ 39401u3t6
+ 40878u4t5
+ 57956u5t4
+ 72977u6t3
+ 56244u7t2
+23121u8t+3840u
9)s11
+2(3000 t
10+20475ut
9+62005u
2t8
+104385u3t7
+118565u4t6
+137297u5t5
+175620u6t4
+170653u7t3
+ 102876u8t2
+ 33792u9t + 4602 u
10)s10
+ 2(2460t
11+ 20475ut
10+ 77358u
2t9
+ 164395 u3t8
+ 215383u4t7
+ 230739u5t6
+ 294815u6t5
+ 356593u7t4
+ 290657 u8t3
+ 140082u9t2
+ 35847u10t + 3840u
11)s9
+(2640 t
12+ 27090ut
11+ 124010u
2t10
+ 328790u3t9
+ 519114u4t8
+ 554262 u5t7
+ 649134u6t6
+ 963078u7t5
+ 1095009u8t4
+ 756156u9t3
+ 291138 u10t2
+ 55904u11t
+ 4367u12)s8
+ 2(420t
13+ 5715u t
12+ 31286u
2t11
+ 104385u3t10
+ 215383u4t9
+ 277131u5t8
+ 300068u6t7
+ 447563u7t6
+661734u8t5
+642258u9t4
+363648 u10t3
+110242u11t2
+15265u12t+774u
13)s7
+(120 t
14+2790ut
13+18489u
2t12
+78802u3t11
+237130u4t10
+461478u5t9
+649134u6t8
+895126u7t7
+1291792u8t6
+1479900 u9t5
+1107162u10t4
+486996u11t3
+111068u12t2
=+10260u13t+259u
14)s6
+2tu(150t
13+1339ut
12+7492u
2t11
+40878u3t10
+137297u4t9
+294815u5t8
+481539u6t7
+661734 u7t6
+ 739950u8t5
+ 608514u9t4
+ 330308u10t3
+ 104819u11
t2
+ 16074u12t + 777u
13)s5
+ t2u2(109t
12+ 850u t
11+ 19215u
2t10
+ 115912u3t9
+ 351240u4t8
+ 713186u5t7
+ 1095009 u6t6
+ 1284516u7t5
+ 1107162u8t4
+ 660616u9t3
+ 249466u10t2
+ 50940u11t
+ 3885u12)s4
+ 2t3u3(− 34t
11+ 1903u t
10+ 18929u
2t9
+ 72977u3t8
+ 170653u4t7
+ 290657u5t6
+ 378078u6t5
+ 363648u7t4
+ 243498u8t3
+ 104819u9t2
+ 25470u10t + 2590 u
11)s3
+ t4u4(t + u)
2(426t
8+ 6892ut
7+ 26549u
2t6
+ 52498u3t5
+ 74207u4t4
+ 79252u5t3
+ 58427u6t2
+ 24378u7t+ 3885 u
8)s2
+ 2t5u5(t+u)
3(308t
6+ 1946ut
5+ 3936u
2t4
+ 5167 u3t3
+ 4537u4t2
+ 2799u5t
+ 777u6)s+ t
6u6(t+ u)
4(259 t
4+ 512ut
3+ 765u
2t2
+ 512u3t+ 259u
4))H(0, z)H(2, y) (s+ u)
2+ 3s
2t2(s+ t)
6u2(t+ u)
6(363s
8
+ 726(t+ 3u)s7
+ 3(363t
2+ 796ut+ 2057u
2)s6
+ 6(121t
3+ 348ut
2+ 480u
2t+ 1815u
3)s5
+(363t
4+ 958ut
3− 297u2t2
+ 1782u3t
+ 13068 u4)s4
+ 2u(246t
4 − 58ut3 − 1296u
2t2
+ 891u3t + 5445 u
4)s3
+ u2(504t
4 − 116ut3 − 297u
2t2
+ 2880u3t + 6171 u
4)s2
– 33 –
=+2u3(246t
4+479ut
3+1044u
2t2
+1194u3t+1089 u
4)s+363u
4(t2
+ut+u2)2)
H(0, 0, z)(s+u)2
+36 s2t2(s+ t)
6u2(t+u)
6(22s
8
+ 44(t+ 3u)s7
+ 2(33t
2+ 70u t+ 187u
2)s6
+(44t
3+ 246ut
2+ 147u
2t+ 660u
3)s5
+(22t
4+ 115ut
3+ 360u
2t2
+ 41u3t+ 792u
4)s4
+u(64t
4+95ut
3+246u
2t2
+2u3t+660u
4)s3
+u2(84 t
4+9ut
3+84u
2t2
+54u3t+374u
4)s2
+u3(54t
4−11u t3
+36u2t2
+63u3t
+ 132u4)s+u
4(18t
4+ 4ut
3+ 18u
2t2
+ 21u3t+ 22u
4))H(0, y)H(0, 0, z)(s+u)
2 − 36s2t2(s+ t)
6u2(t+u)
6(22s
8+ 3(7t+ 44u)s
7
+(18t
2+ 63ut + 374u
2)s6
+(4t
3+ 36ut
2+ 54u
2t + 660u
3)s5
+(18t
4 − 11u t3
+ 84u2t2
+ 2u3t + 792u
4)s4
+ u(54t
4+ 9ut
3
+246u2t2
+41u3t+660u
4)s3
+u2(84t
4+95ut
3+360u
2t2
+147 u3t+374u
4)s2
+u3(64t
4+115ut
3+246u
2t2
+140u3t+132u
4)s
+22u4(t2
+ut+u2)2)
H(2, y)H(0, 0, z) (s+u)2
+18s2t2u2(t+u)
2((
25t4
+64ut3
+78u2t2
+44u3t+11u
4)s14
+2(92t
5+278ut
4
+ 393u2t3
+ 307u3t2
+ 133 u4t+ 27u
5)s13
+(633t
6+ 2332ut
5+ 3918u
2t4
+ 3896u3t3
+ 2351u4t2
+ 816u5t+ 124u
6)s12
+ 2(684t
7
+ 2970u t6
+ 5715u2t5
+ 6827u3t4
+ 5495u4t3
+ 2871u5t2
+ 846u6t+ 96 u
7)s11
+(2094t
8+ 10548ut
7+ 21762u
2t6
+ 27160u3t5
+ 25897u4t4
+ 19800u5t3
+ 10356u6t2
+ 2820u7t + 231u
8)s10
+ 2(1200t
9+ 6984ut
8+ 15768u
2t7
+ 19041u3t6
+ 16319u4t5
= + 14613u5t4
+ 13072u6t3
+ 7593u7t2
+ 2013u8t + 105u
9)s9
+(2094t
10+ 13968ut
9+ 35988u
2t8
+ 47158u3t7
+ 37273u4t6
+ 27528u5t5
+ 31140u6t4
+ 31554u7t3
+ 17931u8t2
+ 4336u9t + 130 u
10)s8
+ 2(684t
11+ 5274ut
10+ 15768u
2t9
+ 23579u3t8
+ 22058u4t7
+ 21537u5t6
+ 26874u6t5
+ 27399u7t4
+ 18504u8t3
+ 7571u9t2
+ 1472u10t + 24u
11)s7
+(633t
12+ 5940u t
11
+ 21762u2t10
+ 38082u3t9
+ 37273u4t8
+ 43074u5t7
+ 83288u6t6
+ 111834u7t5
+ 83094u8t4
+ 33834u9t3
+ 7744u10t2
+ 1056u11t
+ 8u12)s6
+ 2t(92t
12+ 1166ut
11+ 5715u
2t10
+ 13580u3t9
+ 16319u4t8
+ 13764u5t7
+ 26874u6t6
+ 55917u7t5
+ 62742u8t4
+ 36199u9t3
+ 9748u10t2
+ 930u11t + 72 u
12)s5
+ t2(25t
12+ 556ut
11+ 3918u
2t10
+ 13654u3t9
+ 25897u4t8
+ 29226u5t7
+ 31140u6t6
+ 54798u7t5
+ 83094u8t4
+ 72398u9t3
+ 32492u10t2
+ 6012u11t + 84u
12)s4
+ 2t3u(32t
11+ 393ut
10+ 1948u
2t9
+5495u3t8
+9900u4t7
+13072 u5t6
+15777u6t5
+18504u7t4
+16917u8t3
+9748u9t2
+3006u10t+368u
11)s3
+ t4u2(t+u)
2(78t
8
+ 458ut7
+ 1357u2t6
+ 2570u3t5
+ 3859u4t4
+ 4898u5t3
+ 4276u6t2
+ 1692u7t+ 84 u
8)s2
+ 2t5u3(t+u)
3(22t
6+ 67ut
5+ 141u
2t4
+ 200u3t3
+ 320u4t2
+ 312u5t + 72u
6)s + t
6u4(t + u)
4(11t
4+ 10u t
3+ 18u
2t2
+ 16u3t + 8u
4))H(0, z)H(0, 2, y)(s + u)
2
= + 3t2
(s+ t)u2((
17t6
+ 1338ut5
+ 1209u2t4
+ 3688u3t3
+ 4269u4t2
+ 762u5t+ 293u
6)s15
+ (t+u)2(125t
5+ 9282ut
4− 1574 u2t3
+ 24402u3t2
+ 2031u4t + 1740u
5)s14
+(421t
8+ 28668 ut
7+ 79874u
2t6
+ 122578u3t5
+ 210974u4t4
+ 216624u5t3
+ 90402u6t2
+18674u7t+4873u
8)s13
+(t+u)2(853t
7+47050u t
6+99979u
2t5
+64212u3t4
+244839u4t3
+99258u5t2
+22313u6t+8520u
7)s12
+ 4(288t
10+ 12551ut
9+ 71057u
2t8
+ 139212 u3t7
+ 179702u4t6
+ 266064u5t5
+ 276429u6t4
+ 139626u7t3
+ 41347 u8t2
+ 13917u9t
+ 2547u10)s11
+ 2(t + u)2(546t
9+ 13510 ut
8+ 92097u
2t7
+ 124154u3t6
+ 79909u4t5
+ 282798u5t4
+ 136349u6t3
+ 25806u7t2
+17949u8t+4260u
9)s10
+(745t
12+5476u t
11+88790u
2t10
+380158u3t9
+559919u4t8
+624124u5t7
+1280316 u6t6
+1630684u7t5
+ 908135u8t4
+ 264280u9t3
+ 94614u10t2
+ 32670 u11t + 4873u
12)s9
+ (t + u)2(361t
11 − 5942ut10 − 13109 u
2t9
+ 45310u3t8
− 83270u4t7 − 225424u
5t6
+ 359776u6t5
+ 341850u7t4
+ 131133u8t3
+ 49098u9t2
+ 8565u10t+ 1740u
11)s8
+(113t
14 − 5422ut13
− 49927u2t12 − 155092u
3t11 − 318038 u
4t10 − 778482u
5t9 − 1327656u
6t8 − 974758u
7t7 − 19040u
8t6
+ 432306u9t5
+ 380872u10t4
= + 185882u11t3
+ 39939u12t2
+ 2122 u13t + 293u
14)s7
+ t(t + u)2(17t
12 − 2466ut11 − 25660 u
2t10 − 88158u
3t9 − 136236u
4t8
−237708u5t7−370210u
6t6−209898 u
7t5−117978u
8t4−9304u
9t3
+43600u10t2
+14262u11t+49 u
12)s6− t2u
(424t
13+9046ut
12
+ 64296u2t11
+ 209881u3t10
+ 368916u4t9
+ 405336u5t8
+ 306108u6t7
+ 185900 u7t6
+ 201510u8t5
+ 255266u9t4
+ 158896u10t3
+ 31479u11t2 − 5494u
12t− 2252u
13)s5 − t3u2
(t+ u)2(1038 t
10+ 11826ut
9+ 41953u
2t8
+ 50370u3t7 − 10747u
4t6 − 92766u
5t5
− 113853u6t4 − 35658u
7t3
+ 15137u8t2
+ 11676u9t + 2344 u
10)s4 − t4u3
(t + u)3(1108t
8+ 5303ut
7+ 2515u
2t6 − 23685u
3t5
− 48783u4t4− 46581u
5t3− 17785u
6t2− 2753u
7t− 67 u
8)s3− t5u4
(t+u)4(133t
6− 1574ut5− 8533u
2t4− 14102 u
3t3− 10237u
4t2
− 2876u5t− 167u
6)s2
+ 30t6u5(t + u)
6(10t
3+ 37ut
2+ 37u
2t + 14u
3)s + 120t
7u6(t + u)
6(t2
+ ut + u2))H(1, 0, z)(s + u)
2
= + 18s2t2(s+ t)
2u2((
11t6
+ 162ut5
+ 129u2t4
+ 796u3t3
+ 129u4t2
+ 162u5t+ 11u
6)s12
+ 6(11t
7+ 193ut
6+ 349u
2t5
+ 1047u3t4
+ 1027u4t3
+ 313u5t2
+ 173u6t + 7u
7)s11
+(187 t
8+ 3280ut
7+ 8506u
2t6
+ 20204u3t5
+ 32372u4t4
+ 18608u5t3
+ 6910 u6t2
+ 2596u7t+ 73u
8)s10
+ 2(165t
9+ 2522ut
8+ 8324u
2t7
+ 17309u3t6
+ 35002u4t5
+ 33469u5t4
+ 14236u6t3
+ 6119u7t2
+ 1745u8t
+ 53u9)s9
+(396t
10+ 4920ut
9+ 19227u
2t8
+ 34792u3t7
+ 71793u4t6
+ 105726u5t5
+ 63533u6t4
+ 25164u7t3
+ 13635u8t2
+ 3190u9t + 168u
10)s8
+ 2(165t
11+ 1725u t
10+ 7356u
2t9
+ 10992u3t8
+ 12447u4t7
+ 31129u5t6
+ 30585u6t5
+ 10947u7t4
+9212u8t3
+6186u9t2
+1323u10t+109u
11)s7
+(187t
12+1872ut
11+8220u
2t10
+10632u3t9−15915u
4t8−29212u
5t7−9538u
6t6
− 13152u7t5
+ 1543u8t4
+ 19604u9t3
+ 10518u10t2
+ 2096u11t + 185u
12)s6
+ 2(33 t
13+ 372ut
12+ 1782u
2t11
+ 2908u3t10
− 8202u4t9 − 31332u
5t8 − 35999u
6t7 − 26337u
7t6 − 11010u
8t5
+ 8183u9t4
+ 10293u10
t3
+ 3681u11t2
+ 623u12t + 45u
13)s5
+(11t
14+ 182u t
13+ 1142u
2t12
+ 3266u3t11 − 2041u
4t10 − 30594u
5t9 − 56568 u
6t8 − 48084u
7t7 − 20480u
8t6
+ 13148u9t5
– 34 –
=+25835u10t4
+13918 u11t3
+3530u12t2
+452u13t+19u
14)s4
+2tu(10 t
13+115ut
12+604u
2t11
+1366u3t10−633u
4t9−5650u
5t8
− 5310u6t7
+ 1442u7t6
+ 9166u8t5
+ 12427u9t4
+ 8168u10t3
+ 2766u11t2
+ 499u12t+ 38u
13)s3
+ t2u2(t+ u)
2(24t
10+ 190ut
9
+ 841u2t8
+ 1482u3t7
+ 1601u4t6
+ 4172u5t5
+ 4881u6t4
+ 5362u7t3
+ 3151u8t2
+ 930u9t + 126u
10)s2
+ 2 t3u3(t + u)
3(10t
8
+ 70ut7
+ 248u2t6
+ 399u3t5
+ 669u4t4
+ 647u5t3
+ 545u6t2
+ 236u7t+ 48u
8)s+ t
4u4(t+ u)
6(11t
4+ 22ut
3+ 39u
2t2
+ 28u3t
+ 33u4))H(0, y) H(1, 0, z)(s+ u)
2+ 18s
2t2(s+ t)
2u2(4(2t
6+ 36ut
5+ 21u
2t4
+ 184u3t3
+ 21u4t2
+ 36u5t+ 2u
6)s12
+ 12(4t
7
+ 88u t6
+ 155u2t5
+ 501u3t4
+ 501u4t3
+ 155u5t2
+ 88u6t+ 4u
7)s11
+ 2(65t
8+ 1472ut
7+ 3872u
2t6
+ 9748u3t5
+ 16246u4t4
+ 9748u5t3
+ 3872u6t2
+ 1472u7t+ 65u
8)s10
+ 2(105 t
9+ 2168ut
8+ 7571u
2t7
+ 16917u3t6
+ 36199u4t5
+ 36199u5t4
+ 16917 u6t3
+7571u7t2
+2168u8t+105u
9)s9
+3(77t
10+1342u t
9+5977u
2t8
+12336u3t7
+27698u4t6
+41828u5t5
+27698u6t4
+12336u7t3
+ 5977u8t2
+ 1342u9t+ 77u
10)s8
+ 6(32 t
11+ 470ut
10+ 2531u
2t9
+ 5259u3t8
+ 9133u4t7
+ 18639u5t6
+ 18639u6t5
+ 9133u7t4
= + 5259u8t3
+ 2531u9t2
+ 470u10t+ 32 u
11)s7
+ 4(31t
12+ 423ut
11+ 2589u
2t10
+ 6536u3t9
+ 7785u4t8
+ 13437u5t7
+ 20822u6t6
+ 13437u7t5
+ 7785u8t4
+ 6536 u9t3
+ 2589u10t2
+ 423u11t+ 31u
12)s6
+ 6(9 t
13+ 136ut
12+ 957u
2t11
+ 3300u3t10
+ 4871u4t9
+ 4588u5t8
+ 7179u6t7
+ 7179u7t6
+ 4588u8t5
+ 4871u9t4
+ 3300u10t3
+ 957 u11t2
+ 136u12t + 9u
13)s5
+(11t
14+ 266u t
13
+2351u2t12
+10990u3t11
+25897u4t10
+32638u5t9
+37273 u6t8
+44116u7t7
+37273u8t6
+32638u9t5
+25897u10t4
+10990 u11t3
+2351u12t2
+266u13t+11u
14)s4
+2tu(22 t
13+307ut
12+1948u
2t11
+6827u3t10
+13580u4t9
+19041u5t8
+23579u6t7
+23579u7t6
+ 19041u8t5
+ 13580u9t4
+ 6827u10t3
+ 1948u11t2
+ 307u12t+ 22u
13)s3
+ 6t2u2(t+ u)
2(13t
10+ 105ut
9+ 430u
2t8
+ 940u3t7
+ 1317u4t6
+ 1682u5t5
+ 1317u6t4
+ 940u7t3
+ 430u8t2
+ 105u9t+ 13u
10)s2
+ 4 t3u3(t+ u)
3(16t
8+ 91ut
7+ 262u
2t6
+ 410u3t5
+530u4t4
+410u5t3
+262u6t2
+91u7t+16u
8)s+ t
4u4(t+u)
6(25t
4+34ut
3+54u
2t2
+34u3t+25u
4))H(0, z) H(2, 0, y)(s+u)
2
= + 18s2t2u2(6(11t
6+ 46ut
5+ 156u
2t4
+ 102u3t3
+ 156u4t2
+ 46u5t + 11u
6)s14
+ 2(270 t
7+ 1259ut
6+ 4389u
2t5
+ 4796u3t4
+5120u4t3
+3729u5t2
+1049u6t+204u
7)s13
+(2055t
8+10770ut
7+38032u
2t6
+57306u3t5
+58498u4t4
+54214u5t3
+27450u6t2
+ 7450u7t+ 1185u
8)s12
+ 2(2410t
9+ 14457ut
8+ 51810u
2t7
+ 97505u3t6
+ 109719u4t5
+ 108252u5t4
+ 77806u6t3
+ 32031u7t2
+8199u8t+1059u
9)s11
+(7744t
10+53588ut
9+198480u
2t8
+439066u3t7
+579501 u4t6
+598332u5t5
+517783u6t4
+294682u7t3
+ 105495u8t2
+ 24196 u9t + 2541u
10)s10
+ 2(4458t
11+ 35621ut
10+ 138966 u
2t9
+ 344982u3t8
+ 538700u4t7
+ 609874u5t6
+ 590760u6t5
+ 426236 u7t4
+ 200386u8t3
+ 62613u9t2
+ 12146u10t + 1050u
11)s9
+(7450t
12+ 68928ut
11+ 290076u
2t10
+ 782276u3t9
+ 1406634u4t8
+ 1787400u5t7
+ 1901521u6t6
+ 1654302u7t5
+ 999621 u8t4
+ 402156u9t3
+ 106839u10t2
+ 16578u11t
+ 1179u12)s8
+ 2(2230t
13+ 24137ut
12+ 113268u
2t11
+ 330723u3t10
+ 666867u4t9
+ 948111u5t8
+ 1082558u6t7
+ 1072690u7t6
= + 809304 u8t5
+ 421377u9t4
+ 148590u10t3
+ 32739u11t2
+ 3807u12t + 207 u
13)s7
+(1830t
14+ 23864ut
13+ 129744u
2t12
+ 419622 u3t11
+ 946629u4t10
+ 1526944u5t9
+ 1879479u6t8
+ 1986148u7t7
+ 1729402u8t6
+ 1108500u9t5
+ 506934u10t4
+ 157722u11
t3
+ 28413u12t2
+ 2220u13t + 69u
14)s6
+ 2t(232 t
14+ 3972ut
13+ 26409u
2t12
+ 97770u3t11
+ 247866u4t10
+ 463269u5t9
+ 652628u6t8
+ 749862u7t7
+ 712998u8t6
+ 514895 u9t5
+ 272466u10t4
+ 106176u11t3
+ 28022u12t2
+ 3996u13
t
+ 159u14)s5
+ t2(55t
14+ 1614ut
13+ 14748u
2t12
+ 66434u3t11
+ 190555u4t10
+ 406308u5t9
+ 671989u6t8
+ 896290u7t7
+ 978039u8t6
+ 811640u9t5
+ 480198u10t4
+ 201792 u11t3
+ 59561u12t2
+ 11310u13t + 1083u
14)s4
+ 2t3u(74t
13+ 1262ut
12
+ 7944u2t11
+ 27682u3t10
+ 67049u4t9
+ 125496u5t8
+ 189647u6t7
+ 237429u7t6
+ 234672u8t5
+ 169330u9t4
+ 85057u10t3
+ 28209u11t2
+ 5389u12t + 424u
13)s3
+ t4u2(t + u)
2(192t
10+ 1868ut
9+ 7244u
2t8
+ 17304u3t7
+ 30738u4t6
+ 40806u5t5
+ 45573u6t4
+ 36880u7t3
+ 20764u8t2
+ 7278u9t+ 1137u
10)s2
+ 2t5u3(t+u)
3(64t
8+ 420u t
7+ 1164u
2t6
+ 2189u3t5
+ 2787u4t4
+ 2772u5t3
+ 1870u6t2
+ 855u7t + 183u
8)s + t
6u4(t + u)
6(47t
4+ 64ut
3+ 117u
2t2
+ 92u3t + 83u
4))H(0, 1, 0, z)(s + u)
2
– 35 –
= + 36s2t2(s + t)
6u2(t + u)
6(22s
8+ 44(t + 3u)s
7+ 2
(33t
2+ 70ut + 187u
2)s6
+(44t
3+ 246ut
2+ 147u
2t + 660u
3)s5
+(22t
4
+ 115u t3
+ 360u2t2
+ 41u3t + 792u
4)s4
+ u(64t
4+ 95ut
3+ 246u
2t2
+ 2u3t + 660u
4)s3
+ u2(84t
4+ 9ut
3+ 84u
2t2
+ 54u3t
+ 374u4)s2
+ u3(54t
4 − 11ut3
+ 36u2t2
+ 63u3t + 132 u
4)s + u
4(18t
4+ 4ut
3+ 18u
2t2
+ 21u3t + 22 u
4))H(1, 0, 0, z)(s + u)
2
+ 36s2t2u3((
48t5 − 6u t
4+ 332u
2t3
+ 45u3t2
+ 90u4t + 11u
5)s14
+(420t
6+ 282u t
5+ 2684u
2t4
+ 2292u3t3
+ 810u4t2
+ 542u5t + 42u
6)s13
+(1386t
7+ 1149ut
6+ 7038u
2t5
+ 12044u3t4
+ 4972u4t3
+ 2592u5t2
+ 1202u6t + 73u
7)s12
+(2181t
8 − 6ut7
+ 3 u2t6
+ 15414u3t5
+ 7299u4t4 − 896u
5t3
+ 2931u6t2
+ 1368u7t + 106 u
8)s11
+(985t
9 − 9867ut8
− 44480u2t7 − 48559u
3t6 − 45186 u
4t5 − 50331u
5t4 − 19580u
6t3
+ 585u7t2
+ 1097u8t + 168u
9)s10 −
(2469t
10+ 31352ut
9
+ 135204u2t8
+ 241022u3t7
+ 253354 u4t6
+ 222072u5t5
+ 127806u6t4
+ 30846u7t3
+ 657u8t2 − 980u
9t− 218u
10)s9
−(5517t
11+ 52233ut
10+ 228083u
2t9
+ 506619u3t8
+ 645063u4t7
+ 575952u5t6
+ 368997u6t5
+ 131304u7t4
+ 16832u8t3
− 1527u9t2 − 936u
10t− 185u
11)s8 −
(5797 t
12+ 55314ut
11+ 250929u
2t10
+ 646444u3t9
+ 990366u4t8
+ 1001980u5t7
+ 717884u6t6
+ 319380u7t5
+ 58843u8t4 − 6082u
9t3 − 4017u
10t2 − 684u
11t− 90u
12)s7 −
(3849 t
13+ 40039ut
12+ 191778u
2t11
= + 546879u3t10
+ 969791u4t9
+ 1126182u5t8
+ 922078u6t7
+ 512534u7t6
+ 148569u8t5 − 1403u
9t4 − 14004u
10t3 − 3726u
11t2
−315u12t−19u
13)s6−t
(1647t
13+19818ut
12+104248u
2t11
+323862u3t10
+638973 u4t9
+819288u5t8
+723606u6t7
+455700u7t6
+180305u8t5
+24144 u9t4−13260u
10t3−8070u
11t2−1683u
12t−66u
13)s5− t2
(413t
13+6240ut
12+38435u
2t11
+133574u3t10
+291906u4t9
+405133u5t8
+357472u6t7
+200055u7t6
+58195u8t5−7313u
9t4−13779u
10t3−6238u
11t2−1920u
12t−309 u
13)s4
− t3(48t
13+ 1112ut
12+ 8730u
2t11
+ 35276 u3t10
+ 86245u4t9
+ 130602u5t8
+ 113599u6t7
+ 38248u7t6 − 30777 u
8t5 − 50450u
9t4
− 31999u10t3 − 10602u
11t2 − 1774u
12t− 114 u
13)s3 − t4u(t+u)
2(84t
10+ 898ut
9+ 3400u
2t8
+ 6309 u3t7
+ 5217u4t6 − 2505u
5t5
−8514u6t4−9343u
7t3−5743u
8t2−2007u
9t−336u
10)s2−t5u2
(t+u)3(48t
8+200u t
7+135u
2t6−571u
3t5−1726u
4t4−1854u
5t3
−1219u6t2−459u
7t−90u
8)s+t
6u4(t+u)
6(23t
3+54ut
2+46u
2t+26 u
3))H(1, 1, 0, z)(s+u)
2+9(s+t)
2u2(t+u)
(2(92 t
7+224ut
6
+ 807u2t5
+ 41u3t4
+ 227u4t3
+ 71u5t2
+ 70u6t+ 20 u
7)s15
+ 2(548t
8+ 1800ut
7+ 6507u
2t6
+ 5556u3t5
+ 2001 u4t4
+ 2149u5t3
+864u6t2
+535u7t+120u
8)s14
+(3080 t
9+12672ut
8+43909u
2t7
+68677u3t6
+39172u4t5
+27176u5t4
+19411u6t3
+8427u7t2
+ 3620u8t+ 640u
9)s13
+(5400 t
10+ 26796ut
9+ 85362u
2t8
+ 182471u3t7
+ 168303u4t6
+ 105098u5t5
+ 92562u6t4
+ 53097u7t3
+21885u8t2
+7050u9t+1000u
10)s12
+(6464t
11+38196ut
10+114563u
2t9
+283713u3t8
+385450 u4t7
+275704u5t6
+227431u6t5
=+183473u7t4
+90148u8t3
+33770u9t2
+8600u10t+1000u
11)s11
+(5400t
12+38196u t
11+123420u
2t10
+320669u3t9
+573417u4t8
+513000u5t7
+343086 u6t6
+321375u7t5
+218509u8t4
+96742u9t3
+32200u10t2
+6690 u11t+640u
12)s10
+(3080t
13+26796ut
12
+ 114563 u2t11
+ 320669u3t10
+ 641380u4t9
+ 698714u5t8
+ 386310u6t7
+ 282028u7t6
+ 279284u8t5
+ 162550u9t4
+ 65139u10t3
+ 18779 u11t2
+ 3220u12t + 240u
13)s9
+(1096t
14+ 12672u t
13+ 85362u
2t12
+ 283713u3t11
+ 573417u4t10
+ 698714u5t9
+ 392272u6t8
+ 129314u7t7
+ 178058u8t6
+ 158492u9t5
+ 72298u10t4
+ 25025u11t3
+ 6257u12t2
+ 870u13t+ 40u
14)s8
+ t(184t
14
+ 3600ut13
+ 43909u2t12
+ 182471u3t11
+ 385450u4t10
+ 513000u5t9
+ 386310u6t8
+ 129314u7t7
+ 92160u8t6
+ 110380u9t5
+ 48211u10t4
+ 11865u11t3
+ 3700u12t2
+ 994u13t + 100 u
14)s7
+ t2u(448t
13+ 13014ut
12+ 68677u
2t11
+ 168303u3t10
+275704u4t9
+343086u5t8
+282028u6t7
+178058 u7t6
+110380u8t5
+33784u9t4−4267u
10t3−3791u
11t2−474 u
12t+42u
13)s6
+ t3u2(1614t
12+ 11112ut
11+ 39172 u
2t10
+ 105098u3t9
+ 227431u4t8
+ 321375u5t7
+ 279284u6t6
+ 158492u7t5
+ 48211u8t4
− 4267u9t3 − 7188u
10t2 − 1770u
11t− 164u
12)s5
+ t4u3(82t
11+ 4002ut
10+ 27176u
2t9
+ 92562u3t8
+ 183473u4t7
+ 218509u5t6
+ 162550u6t5
+ 72298u7t4
+ 11865u8t3 − 3791u
9t2 − 1770u
10t− 204u
11)s4
+ t5u4
(t + u)2(454t
8+ 3390ut
7+ 12177u
2t6
+ 25353u3t5
+ 27265u4t4
+ 16859u5t3
+ 4156u6t2 − 146u
7t− 164u
8)s3
+ t6u5(t+ u)
3(142t
6+ 1302ut
5+ 4095u
2t4
+ 5552u3t3
+ 3527u4t2
+ 868u5t+ 42 u
6)s2
+ 10t7u6(t+u)
5(14t
3+ 37ut
2+ 37u
2t+ 10 u
3)s+ 40t
8u7(t+u)
5(t2
+ut+u2))H(1, 0, y) (s+u)
=− 3s2(s+ t)
2u2(t+ u)
2((
259t6
+ 616ut5
+ 426u2t4 − 68 u
3t3
+ 109u4t2
+ 300u5t+ 120u
6)s14
+ 2(774t
7+ 2870u t
6+ 3872u
2t5
+1903u3t4
+425u4t3
+1339u5t2
+1395u6t+420 u
7)s13
+(4367t
8+21396ut
7+40759u
2t6
+37858u3t5
+19215u4t4
+14984u5t3
+ 18489u6t2
+ 11430u7t + 2640u
8)s12
+ 2(3840t
9+ 23121ut
8+ 56244u
2t7
+ 72977u3t6
+ 57956u4t5
+ 40878u5t4
+ 39401u6t3
+31286u7t2
+13545u8t+2460u
9)s11
+2(4602t
10+33792ut
9+102876u
2t8
+170653u3t7
+175620 u4t6
+137297u5t5
+118565u6t4
+ 104385u7t3
+ 62005u8t2
+ 20475u9t + 3000u
10)s10
+ 2(3840t
11+ 35847ut
10+ 140082u
2t9
+ 290657u3t8
+ 356593u4t7
+ 294815u5t6
+ 230739u6t5
+ 215383u7t4
+ 164395u8t3
+ 77358u9t2
+ 20475u10t + 2460u
11)s9
+(4367t
12+ 55904ut
11
+ 291138u2t10
+ 756156u3t9
+ 1095009u4t8
+ 963078u5t7
+ 649134u6t6
+ 554262u7t5
+ 519114u8t4
+ 328790u9t3
+ 124010u10t2
+ 27090u11t + 2640u
12)s8
+ 2(774t
13+ 15265ut
12+ 110242u
2t11
+ 363648u3t10
+ 642258 u4t9
+ 661734u5t8
+ 447563u6t7
+300068u7t6
+277131u8t5
+215383 u9t4
+104385u10t3
+31286u11t2
+5715u12t+420u
13)s7
+(259t
14+10260ut
13+111068u
2t12
– 36 –
=+486996u3t11
+1107162u4t10
+1479900u5t9
+1291792u6t8
+895126u7t7
+649134u8t6
+461478u9t5
+237130u10t4
+78802u11t3
+ 18489 u12t2
+ 2790u13t + 120u
14)s6
+ 2tu(777t
13+ 16074 ut
12+ 104819u
2t11
+ 330308u3t10
+ 608514u4t9
+ 739950u5t8
+ 661734u6t7
+ 481539u7t6
+ 294815u8t5
+ 137297u9t4
+ 40878u10
t3
+ 7492u11t2
+ 1339u12t + 150u
13)s5
+ t2u2(3885 t
12
+ 50940ut11
+ 249466u2t10
+ 660616u3t9
+ 1107162u4t8
+ 1284516u5t7
+ 1095009u6t6
+ 713186u7t5
+ 351240u8t4
+ 115912u9t3
+ 19215u10t2
+ 850u11t + 109u
12)s4
+ 2t3u3(2590 t
11+ 25470ut
10+ 104819u
2t9
+ 243498u3t8
+ 363648u4t7
+ 378078 u5t6
+ 290657u6t5
+ 170653u7t4
+ 72977u8t3
+ 18929u9t2
+ 1903 u10t− 34u
11)s3
+ t4u4(t + u)
2(3885t
8+ 24378u t
7+ 58427u
2t6
+ 79252u3t5
+ 74207u4t4
+ 52498u5t3
+ 26549u6t2
+ 6892u7t+ 426u
8)s2
+ 2t5u5(t+u)
3(777t
6+ 2799u t
5+ 4537u
2t4
+ 5167u3t3
+3936u4t2
+1946u5t+308u
6)s+ t
6u6(t+u)
4(259t
4+512ut
3+765u
2t2
+512u3t+259 u
4))H(0, y)H(1, z)+9s
2(t+u)
2(2(20t
8
+ 50u t7
+ 21u2t6− 82u
3t5− 102u
4t4− 82u
5t3
+ 21u6t2
+ 50u7t+ 20 u
8)s16
+ 2(140t
9+ 505ut
8+ 568u
2t7− 298u
3t6− 1069u
4t5
− 1069u5t4 − 298u
6t3
+ 568u7t2
+ 505u8t + 140u
9)s15
+(880t
10+ 4370ut
9+ 8221u
2t8
+ 4262u3t7 − 6199u
4t6 − 10932u
5t5
−6199u6t4
+4262u7t3
+8221u8t2
+4370u9t+880 u
10)s14
+2(820t
11+5395ut
10+14563u
2t9
+17988 u3t8
+5650u4t7−8508u
5t6
=− 8508u6t5
+ 5650u7t4
+ 17988u8t3
+ 14563u9t2
+ 5395u10t+ 820u
11)s13
+(2000 t
12+ 16930ut
11+ 60889u
2t10
+ 115200u3t9
+112888u4t8
+52018 u5t7
+18062u6t6
+52018u7t5
+112888u8t4
+115200u9t3
+60889 u10t2
+16930u11t+2000u
12)s12
+2(820t
13
+ 8825 ut12
+ 40630u2t11
+ 106430u3t10
+ 162506u4t9
+ 145433u5t8
+ 94054u6t7
+ 94054u7t6
+ 145433u8t5
+ 162506u9t4
+ 106430u10
t3
+ 40630u11t2
+ 8825u12t + 820u
13)s11
+(880 t
14+ 12310ut
13+ 71305u
2t12
+ 252860u3t11
+ 542940u4t10
+ 672624u5t9
+ 495141u6t8
+ 346704u7t7
+ 495141u8t6
+ 672624 u9t5
+ 542940u10t4
+ 252860u11t3
+ 71305u12t2
+ 12310u13
t
+ 880u14)s10
+ 2(140t
15+ 2785ut
14+ 20491u
2t13
+ 99450u3t12
+ 294436u4t11
+ 490859u5t10
+ 448931u6t9
+ 254956u7t8
+254956u8t7
+448931u9t6
+490859u10t5
+294436 u11t4
+99450u12t3
+20491u13t2
+2785u14t+140u
15)s9
+(40t
16+1490ut
15
+14845u2t14
+102820u3t13
+419280 u4t12
+950788u5t11
+1225773u6t10
+975710u7t9
+743060u8t8
+975710u9t7
+1225773u10t6
+950788u11t5
+419280u12t4
+102820u13t3
+14845u14t2
+1490u15t+40u
16)s8
+2 tu(90t
15+1540ut
14+16932u
2t13
+96123u3t12
+ 304282 u4t11
+ 583798u5t10
+ 762212u6t9
+ 803305u7t8
+ 803305u8t7
+ 762212u9t6
+ 583798u10t5
+ 304282u11t4
+ 96123u12t3
+ 16932u13t2
+ 1540u14t + 90u
15)s7
+ t2u2(282 t
14+ 6622ut
13+ 54887u
2t12
+ 264008u3t11
+ 776536u4t10
+ 1517240u5t9
+ 2171441u6t8
+ 2431080u7t7
+ 2171441u8t6
+ 1517240u9t5
+ 776536u10t4
+ 264008u11t3
+ 54887u12t2
+ 6622u13t+ 282u
14)s6
= + 2t3u3(298t
13+ 4418u t
12+ 40731u
2t11
+ 190625u3t10
+ 505964u4t9
+ 877790u5t8
+ 1117090u6t7
+ 1117090u7t6
+ 877790u8t5
+ 505964u9t4
+ 190625 u10t3
+ 40731u11t2
+ 4418u12t + 298u
13)s5
+ t4u4(536t
12+ 16810ut
11+ 131975u
2t10
+ 463360u3t9
+ 936996u4t8
+ 1292362u5t7
+ 1406138u6t6
+ 1292362u7t5
+ 936996u8t4
+ 463360 u9t3
+ 131975u10t2
+ 16810u11t+ 536u
12)s4
+ 2t5u5(848t
11+ 13094ut
10+ 64600u
2t9
+ 162207u3t8
+ 255217u4t7
+ 298424u5t6
+ 298424u6t5
+ 255217u7t4
+ 162207u8t3
+ 64600u9t2
+ 13094u10t + 848u
11)s3
+ t6u6(t + u)
2(2062 t
8+ 13122ut
7+ 32971u
2t6
+ 48846u3t5
+ 54292u4t4
+ 48846u5t3
+ 32971u6t2
+ 13122u7t + 2062u
8)s2
+ 4t7u7(t + u)
3(158t
6+ 746ut
5+ 1500u
2t4
+ 1923u3t3
+ 1500u4t2
+ 746u5t + 158 u
6)s
+8t8u8(t+u)
4(23t
4+45ut
3+67u
2t2
+45u3t+23 u
4))H(1, z)H(3, y)+3s
2(s+t)u
2(t+u)
2((
17 t6−424ut
5−1038u2t4−1108u
3t3
−133u4t2
+300u5t+120u
6)s15
+(113t
7−2432ut6−9046u
2t5−13902u
3t4−8627u
4t3
+1042 u5t2
+2910u6t+840u
7)s14
+(361t
8
−5422ut7−30575u
2t6−64296u
3t5−66643u
4t4−21748u
5t3
+14031u6t2
+12270u7t+2640 u
8)s13
+(745t
9−5220ut8−49927u
2t7
− 141944u3t6 − 209881u
4t5 − 146102u
5t4 − 877u
6t3
+ 57146u7t2
+ 29730u8t + 4920 u
9)s12
+ 2(546t
10+ 2738ut
9 − 12316u2t8
−77546u3t7−169106u
4t6−184458u
5t5−65973u
6t4
+53495u7t3
+62003u8t2
+22935u9t+3000u
10)s11
+2(576t
11+14602u t
10
=+44395u2t9
+6575u3t8−159019u
4t7−299169u
5t6−202668u
6t5
+31945u7t4
+130735u8t3
+82071u9t2
+23475u10t+2460 u
11)s10
+(853t
12+ 50204ut
11+ 239326u
2t10
+ 380158u3t9 − 5759u
4t8 − 778482u
5t7 − 981862u
6t6 − 306108u
7t5
+ 310132u8t4
+ 327562u9t3
+ 138034u10t2
+ 32010u11t + 2640 u
12)s9
+(421t
13+ 48756ut
12+ 284228u
2t11
+ 643716 u3t10
+ 559919u4t9
− 346654u5t8 − 1327656u
6t7 − 1188026u
7t6 − 185900u
8t5
+ 356130u9t4
+ 244634u10t3
+ 72974u11t2
+ 14070 u12t + 840u
13)s8
+(125t
14+ 28668ut
13+ 194932u
2t12
+ 556848u3t11
+ 840628u4t10
+ 624124u5t9 − 174342u
6t8 − 974758u
7t7 − 907984u
8t6
−201510u9t5
+170032u10t4
+108262 u11t3
+22743u12t2
+3630u13t+120u
14)s7
+t(17 t
14+9532ut
13+79874u
2t12
+311220u3t11
+ 718808u4t10
+ 1133540u5t9
+ 1280316u6t8
+ 835978u7t7 − 19040u
8t6 − 455158 u
9t5 − 255266u
10t4 − 6292u
11t3
+ 26245u12t2
+ 3544u13t+ 420 u
14)s6
+ t2u(1338t
13+ 17115ut
12+ 122578u
2t11
+ 473242u3t10
+ 1064256u4t9
+ 1563708u5t8
+ 1630684u6t7
+ 1174609u7t6
+ 432306u8t5 − 92986u
9t4 − 158896u
10t3 − 40833 u
11t2
+ 2954u12t + 167u
13)s5
+ t3u2(1209 t
12+ 30536ut
11
+ 210974u2t10
+ 653148u3t9
+ 1105716u4t8
+ 1162604u5t7
+ 908135u6t6
+ 653214u7t5
+ 380872u8t4
+ 92158u9t3 − 31479u
10t2
− 16364u11t + 67u
12)s4
+ t4u3(3688 t
11+ 49261ut
10+ 216624u
2t9
+ 465668u3t8
+ 558504u4t7
+ 411820 u5t6
+ 264280u6t5
– 37 –
= + 237894u7t4
+ 185882u8t3
+ 72173u9t2
+ 5494 u10t− 2344u
11)s3
+ t5u4(t+ u)
2(4269t
8+ 21666u t
7+ 42801u
2t6
+ 45136u3t5
+ 32315u4t4
+ 22162u5t3
+ 17975u6t2
+ 9856u7t+ 2252u
8)s2
+ t6u5(t+u)
3(762t
6+ 3225u t
5+ 6713u
2t4
+ 8777u3t3
+ 5973u4t2
+1975u5t+49u
6)s+t
7u6(t+u)
4(293t
4+568ut
3+843u
2t2
+568u3t+293 u
4))H(0, 1, z)+18s
2t2(s+t)
2u2(t+u)
2((
11 t4
+20ut3
+24u2t2
+20u3t+11u
4)s14
+2(33t
5+91u t
4+115u
2t3
+119u3t2
+100u4t+44u
5)s13
+(187t
6+744 ut
5+1142u
2t4
+1208u3t3
+ 1245u4t2
+ 976u5t + 336u
6)s12
+ 2(165t
7+ 936ut
6+ 1782u
2t5
+ 1633u3t4
+ 1366u4t3
+ 1677 u5t2
+ 1363u6t + 406u
7)s11
+(396t
8+ 3450ut
7+ 8220u
2t6
+ 5816u3t5 − 2041u
4t4 − 1266u
5t3
+ 5406u6t2
+ 5360u7t + 1391 u
8)s10
+ 2(165t
9+ 2460ut
8
+ 7356u2t7
+ 5316u3t6 − 8202 u
4t5 − 15297u
5t4 − 5650u
6t3
+ 4428u7t2
+ 4099u8t+ 897u
9)s9
+(187t
10+ 5044ut
9+ 19227u
2t8
+ 21984u3t7 − 15915u
4t6 − 62664u
5t5 − 56568u
6t4 − 10620u
7t3
+ 14826u8t2
+ 9784u9t + 1783 u
10)s8
+ 2(33t
11+ 1640ut
10
+ 8324u2t9
+ 17396u3t8
+ 12447u4t7 − 14606u
5t6 − 35999u
6t5 − 24042u
7t4
+ 1442u8t3
+ 9648u9t2
+ 4481u10t + 668u
11)s7
+(11t
12+ 1158u t
11+ 8506u
2t10
+ 34618u3t9
+ 71793u4t8
+ 62258u5t7 − 9538u
6t6 − 52674u
7t5 − 20480u
8t4
+ 18332u9t3
+ 18756u10t2
+ 6076u11
t + 702u12)s6
+ 2u(81t
12+ 1047ut
11+ 10102u
2t10
+ 35002u3t9
+ 52863u4t8
+ 30585u5t7 − 6576u
6t6
=− 11010u7t5
+ 6574u8t4
+ 12427u9t3
+ 6297u10t2
+ 1397u11t+ 113 u
12)s5
+ u2(129t
12+ 6282ut
11+ 32372u
2t10
+ 66938 u3t9
+ 63533u4t8
+ 21894u5t7
+ 1543u6t6
+ 16366u7t5
+ 25835u8t4
+ 16336u9t3
+ 5137u10t2
+ 760u11t + 33u
12)s4
+ 2tu3(398t
11
+3081ut10
+9304u2t9
+14236u3t8
+12582u4t7
+9212 u5t6
+9802u6t5
+10293u7t4
+6959u8t3
+2766u9t2
+591u10t+48 u
11)s3
+t2u4(t+u)
2(129t
8+1620ut
7+3541u
2t6
+3536 u3t5
+3022u4t4
+2792u5t3
+1912u6t2
+746u7t+126u
8)s2
+2t3u5(t+u)
3(81t
6
+276ut5
+227u2t4
+155u3t3
+173u4t2
+112u5t+38u
6)s+ t
4u6(t+u)
4(11t
4−2ut3
+15u2t2
+14u3t+19u
4))H(0, y)H(0, 1, z)
−18s2t2u2(t+u)
2((
47t4
+116ut3
+144u2t2
+96u3t+39u
4)s16
+2(211t
5+697ut
4+1032u
2t3
+886u3t2
+487u4t+147u
5)s15
+ 3(587t
6+ 2466ut
5+ 4371u
2t4
+ 4476u3t3
+ 3059u4t2
+ 1466u5t+ 355u
6)s14
+ 2(2246t
7+ 11795ut
6+ 25344u
2t5
+ 30555u3t4
+ 24384u4t3
+ 14649u5t2
+ 6280u6t+ 1255u
7)s13
+(7761t
8+ 49924ut
7+ 132409u
2t6
+ 195056u3t5
+ 184034u4t4
+ 125820u5t3
+ 68009u6t2
+ 25468u7t + 4325u
8)s12
+ 6(1587t
9+ 12289ut
8+ 40330u
2t7
+ 74208u3t6
+ 86445u4t5
+ 69435 u5t4
+ 42172u6t3
+20076u7t2
+6418u8t+944u
9)s11
+(8447t
10+78224ut
9+319917u
2t8
+731786u3t7
+1046888 u4t6
+1017372u5t5
+727368u6t4
= + 404718u7t3
+ 167685u8t2
+ 44164 u9t + 5599u
10)s10
+ 2(2688t
11+ 30091ut
10+ 156379 u
2t9
+ 443281u3t8
+ 763361u4t7
+878974u5t6
+745371u6t5
+500624 u7t4
+259751u8t3
+91571u9t2
+19006u10t+2015u
11)s9
+3(784t
12+11080ut
11+75305u
2t10
+ 263492u3t9
+ 545731u4t8
+ 746656u5t7
+ 740518u6t6
+ 577912u7t5
+ 364335u8t4
+ 170508u9t3
+ 50345u10t2
+ 7940u11t
+ 660u12)s8
+ 2(318 t
13+ 6360ut
12+ 59340u
2t11
+ 252696u3t10
+ 631038u4t9
+ 1061526u5t8
+ 1285210u6t7
+ 1158562u7t6
+806991u8t5
+444563 u9t4
+181058u10t3
+45120u11t2
+5167u12t+295u
13)s7
+(80t
14+3066ut
13+43714u
2t12
+225298u3t11
+ 680647 u4t10
+ 1441224u5t9
+ 2222801u6t8
+ 2456276u7t7
+ 1932681u8t6
+ 1122364u9t5
+ 510799u10t4
+ 177102u11t3
+37210u12t2
+2790u13t+80u
14)s6
+6tu(58t
13+1689u t
12+11116u
2t11
+42847u3t10
+116103u4t9
+225254u5t8
+308029u6t7
+293932u7t6
+196649u8t5
+94795u9t4
+34537u10t3
+9491u11t2
+1574u12t+58u
13)s5
+t2u2(1092 t
12+11428ut
11+67756u
2t10
+ 245052u3t9
+ 575825u4t8
+ 929600 u5t7
+ 1064520u6t6
+ 875584u7t5
+ 515905u8t4
+ 213096u9t3
+ 59096 u10t2
+ 10508u11t
+ 1092u12)s4
+ 2t3u3(394 t
11+ 5820ut
10+ 29696u
2t9
+ 83756u3t8
+ 156154u4t7
+ 208169u5t6
+ 204213u6t5
+ 148024u7t4
+ 77656u8t3
+ 27425u9t2
+ 5475u10t+ 394u
11)s3
+ 6t4u4(t+u)
2(173t
8+ 987ut
7+ 2643u
2t6
+ 4684u3t5
+ 5690u4t4
+ 4568u5t3
+ 2519u6t2
+ 941u7t + 173 u
8)s2
+ 2t5u5(t + u)
3(150t
6+ 629ut
5+ 1361u
2t4
+ 1851 u3t3
+ 1353u4t2
+ 606u5t + 150u
6)s
+66t6u6(t+u)
4(t2
+ut+u2)2)
H(2, y)H(0, 1, z)−3s2(s+t)
2u2(t+u)
2((
259t6
+616ut5
+426u2t4−68u
3t3
+109u4t2
+300u5t
+ 120u6)s14
+ 2(774t
7+ 2870ut
6+ 3872u
2t5
+ 1903u3t4
+ 425u4t3
+ 1339u5t2
+ 1395u6t + 420u
7)s13
+(4367 t
8+ 21396ut
7
= + 40759u2t6
+ 37858u3t5
+ 19215u4t4
+ 14984u5t3
+ 18489u6t2
+ 11430u7t + 2640u
8)s12
+ 2(3840t
9+ 23121 ut
8+ 56244u
2t7
+ 72977u3t6
+ 57956u4t5
+ 40878u5t4
+ 39401u6t3
+ 31286u7t2
+ 13545u8t+ 2460u
9)s11
+ 2(4602 t
10+ 33792ut
9+ 102876u
2t8
+ 170653u3t7
+ 175620u4t6
+ 137297u5t5
+ 118565u6t4
+ 104385u7t3
+ 62005u8t2
+ 20475u9t + 3000 u
10)s10
+ 2(3840t
11
+ 35847ut10
+ 140082u2t9
+ 290657u3t8
+ 356593u4t7
+ 294815u5t6
+ 230739u6t5
+ 215383u7t4
+ 164395u8t3
+ 77358u9t2
+ 20475u10t + 2460u
11)s9
+(4367t
12+ 55904ut
11+ 291138u
2t10
+ 756156u3t9
+ 1095009u4t8
+ 963078u5t7
+ 649134u6t6
+ 554262u7t5
+ 519114u8t4
+ 328790u9t3
+ 124010u10t2
+ 27090u11t + 2640u
12)s8
+ 2(774t
13+ 15265ut
12+ 110242u
2t11
+ 363648u3t10
+ 642258 u4t9
+ 661734u5t8
+ 447563u6t7
+ 300068u7t6
+ 277131u8t5
+ 215383 u9t4
+ 104385u10t3
+ 31286u11t2
+ 5715u12t + 420u
13)s7
+(259t
14+ 10260ut
13+ 111068u
2t12
+ 486996u3t11
+ 1107162u4t10
+ 1479900u5t9
+ 1291792u6t8
+ 895126u7t7
+ 649134u8t6
+ 461478u9t5
+ 237130u10t4
+ 78802u11t3
+ 18489 u12t2
+ 2790u13t + 120u
14)s6
+ 2tu(777t
13
+ 16074 ut12
+ 104819u2t11
+ 330308u3t10
+ 608514u4t9
+ 739950u5t8
+ 661734u6t7
+ 481539u7t6
+ 294815u8t5
+ 137297u9t4
– 38 –
= + 40878u10
t3
+ 7492u11t2
+ 1339u12t + 150u
13)s5
+ t2u2(3885 t
12+ 50940ut
11+ 249466u
2t10
+ 660616u3t9
+ 1107162u4t8
+ 1284516u5t7
+ 1095009u6t6
+ 713186u7t5
+ 351240u8t4
+ 115912u9t3
+ 19215u10t2
+ 850u11t + 109u
12)s4
+ 2t3u3(2590 t
11
+25470ut10
+104819u2t9
+243498u3t8
+363648u4t7
+378078 u5t6
+290657u6t5
+170653u7t4
+72977u8t3
+18929u9t2
+1903 u10t
−34u11)s3
+t4u4(t+u)
2(3885t
8+24378u t
7+58427u
2t6
+79252u3t5
+74207u4t4
+52498u5t3
+26549u6t2
+6892u7t+426u
8)s2
+2t5u5(t+u)
3(777t
6+2799u t
5+4537u
2t4
+5167u3t3
+3936u4t2
+1946u5t+308u
6)s+ t
6u6(t+u)
4(259t
4+512ut
3+765u
2t2
+512u3t+259 u
4))H(0, 2, y)−18s
2t2u2(t+u)
3(2t(7t
2+15u t+12u
2)s16
+12(8t
4+24ut
3+29u
2t2
+12u3t−u4
)s15
+3(101t
5
+ 423ut4
+ 720u2t3
+ 556u3t2
+ 111 u4t− 31u
5)s14
+(598t
6+ 3066ut
5+ 7134u
2t4
+ 8992u3t3
+ 5154u4t2
+ 510u5t− 318u
6)s13
+(851t
7+ 4495u t
6+ 13290u
2t5
+ 25506u3t4
+ 26949u4t3
+ 12309u5t2
+ 688u6t− 652 u
7)s12
+ 6(158t
8+ 586ut
7+ 2628u
2t6
+ 7708u3t5
+ 11649 u4t4
+ 9092u5t3
+ 3324u6t2
+ 218u7t− 155u
8)s11
+(851 t
9 − 417ut8
+ 9564u2t7
+ 62150u3t6
+ 123813u4t5
+ 121269u5t4
+ 67982 u6t3
+ 23208u7t2
+ 2838u8t− 1002u
9)s10
+ 2(299 t
10 − 2075ut9 − 1896u
2t8
+ 23751u3t7
+ 72903u4t6
+97515u5t5
+71423u6t4
+31963u7t3
+10800u8t2
+1966u9t−409u
10)s9
+3(101t
11−1463ut10−3896u
2t9
+208u3t8
+20429u4t7
= + 58669u5t6
+ 80268u6t5
+ 55172u7t4
+ 19400u8t3
+ 4832u9t2
+ 1000u10t− 156u
11)s8
+ 2(48t
12 − 1128ut11 − 4410 u
2t10
− 17090u3t9 − 31983u
4t8
+ 6084u5t7
+ 100874u6t6
+ 143160 u7t5
+ 88338u8t4
+ 23800u9t3
+ 2622u10t2
+ 582u11t− 81 u
12)s7
+(14t
13 − 572ut12 − 3036u
2t11 − 35818u
3t10 − 106376u
4t9 − 101688u
5t8
+ 48822u6t7
+ 213630u7t6
+ 239397u8t5
+ 134809u9t4
+ 31274u10t3−36u
11t2
+ 157u12t−25 u
13)s6−6tu
(8t
12+ 37ut
11+ 3213u
2t10
+ 11984u3t9
+ 14592u4t8
+ 1987u5t7−12914u
6t6
− 20563u7t5 − 20499u
8t4 − 11612u
9t3 − 2423u
10t2
+ 147u11t + 3u
12)s5
+ t2u2(102t
11 − 5234ut10 − 25530u
2t9 − 39126u
3t8
−12408u4t7
+24648u5t6
+35505u6t5
+40505u7t4
+40476u8t3
+21240u9t2
+3629u10t−267u
11)s4
+2t3u3(−266t
10−1804u t9
− 4752u2t8 − 4830u
3t7
+ 378u4t6
+ 5301u5t5
+ 6806u6t4
+ 6178u7t3
+ 3642u8t2
+ 1119u9t + 156u
10)s3
+ 3t4u4(t + u)
2(16 t
7
− 382ut6 − 532u
2t5
+ 8u3t4
+ 467u4t3
+ 637u5t2
+ 265u6t− 71 u
7)s2 − 2t
5u5(t+u)
3(48t
5+ 151ut
4 − 84u2t3
+ 18u3t2 − 160u
4t
−15u5)s+t
6u7(t+u)
3(12t
3+3ut
2+2u
2t−11u
3))H(1, z)H(0, 3, y)−3s
2(s+ t)
2u2(t+u)
2((
259t6
+616ut5
+426u2t4−68u
3t3
+109u4t2
+300u5t+120u
6)s14
+2(774t
7+2870ut
6+3872u
2t5
+1903u3t4
+425u4t3
+1339u5t2
+1395u6t+420u
7)s13
+(4367 t
8
+ 21396ut7
+ 40759u2t6
+ 37858u3t5
+ 19215u4t4
+ 14984u5t3
+ 18489u6t2
+ 11430u7t + 2640u
8)s12
+ 2(3840t
9+ 23121 ut
8
+ 56244u2t7
+ 72977u3t6
+ 57956u4t5
+ 40878u5t4
+ 39401u6t3
+ 31286u7t2
+ 13545u8t+ 2460u
9)s11
+ 2(4602 t
10+ 33792ut
9
+ 102876u2t8
+ 170653u3t7
+ 175620u4t6
+ 137297u5t5
+ 118565u6t4
+ 104385u7t3
+ 62005u8t2
+ 20475u9t + 3000 u
10)s10
= + 2(3840t
11+ 35847ut
10+ 140082u
2t9
+ 290657u3t8
+ 356593u4t7
+ 294815u5t6
+ 230739u6t5
+ 215383u7t4
+ 164395u8t3
+ 77358u9t2
+ 20475u10t + 2460u
11)s9
+(4367t
12+ 55904ut
11+ 291138u
2t10
+ 756156u3t9
+ 1095009u4t8
+ 963078u5t7
+ 649134u6t6
+ 554262u7t5
+ 519114u8t4
+ 328790u9t3
+ 124010u10t2
+ 27090u11t + 2640u
12)s8
+ 2(774t
13+ 15265ut
12
+ 110242u2t11
+ 363648u3t10
+ 642258 u4t9
+ 661734u5t8
+ 447563u6t7
+ 300068u7t6
+ 277131u8t5
+ 215383 u9t4
+ 104385u10t3
+ 31286u11t2
+ 5715u12t + 420u
13)s7
+(259t
14+ 10260ut
13+ 111068u
2t12
+ 486996u3t11
+ 1107162u4t10
+ 1479900u5t9
+ 1291792u6t8
+ 895126u7t7
+ 649134u8t6
+ 461478u9t5
+ 237130u10t4
+ 78802u11t3
+ 18489 u12t2
+ 2790u13t + 120u
14)s6
+ 2tu(777t
13+ 16074 ut
12+ 104819u
2t11
+ 330308u3t10
+ 608514u4t9
+ 739950u5t8
+ 661734u6t7
+ 481539u7t6
+ 294815u8t5
+ 137297u9t4
+ 40878u10
t3
+ 7492u11t2
+ 1339u12t + 150u
13)s5
+ t2u2(3885 t
12+ 50940ut
11+ 249466u
2t10
+ 660616u3t9
+ 1107162u4t8
+ 1284516u5t7
+ 1095009u6t6
+ 713186u7t5
+ 351240u8t4
+ 115912u9t3
+ 19215u10t2
+ 850u11t + 109u
12)s4
+ 2t3u3(2590 t
11+ 25470ut
10+ 104819u
2t9
+ 243498u3t8
+ 363648u4t7
+ 378078 u5t6
+ 290657u6t5
+ 170653u7t4
+ 72977u8t3
= + 18929u9t2
+ 1903 u10t− 34u
11)s3
+ t4u4(t + u)
2(3885t
8+ 24378u t
7+ 58427u
2t6
+ 79252u3t5
+ 74207u4t4
+ 52498u5t3
+ 26549u6t2
+ 6892u7t + 426u
8)s2
+ 2t5u5(t + u)
3(777t
6+ 2799u t
5+ 4537u
2t4
+ 5167u3t3
+ 3936u4t2
+ 1946u5t + 308u
6)s
+ t6u6(t+ u)
4(259t
4+ 512ut
3+ 765u
2t2
+ 512u3t+ 259 u
4))H(2, 0, y)− 18s
2t2u2(t+ u)
2((
83t4
+ 224u t3
+ 312u2t2
+ 224u3t
+83u4)s16
+(646t
5+2236ut
4+3738 u
2t3
+3738u3t2
+2236u4t+646u
5)s15
+3(795t
6+3434u t
5+6735u
2t4
+8252u3t3
+6735u4t2
+3434u5t+795u
6)s14
+(5590t
7+29722ut
6+68154u
2t5
+96362u3t4
+96362u4t3
+68154u5t2
+29722u6t+5590u
7)s13
+(9297t
8
+ 59792u t7
+ 162893u2t6
+ 265856u3t5
+ 307366u4t4
+ 265856u5t3
+ 162893u6t2
+ 59792u7t+ 9297u
8)s12
+ 6(1912t
9+ 14697ut
8
+ 48146 u2t7
+ 92627u3t6
+ 123322u4t5
+ 123322u5t4
+ 92627u6t3
+ 48146u7t2
+ 14697u8t+ 1912u
9)s11
+(10571t
10+ 97460ut
9
+ 390525 u2t8
+ 895950u3t7
+ 1372200u4t6
+ 1560372u5t5
+ 1372200u6t4
+ 895950u7t3
+ 390525u8t2
+ 97460u9t+ 10571u
10)s10
+ 2(3555t
11+ 40253ut
10+ 202415u
2t9
+ 561210u3t8
+ 989305u4t7
+ 1257298u5t6
+ 1257298u6t5
+ 989305u7t4
+ 561210u8t3
+ 202415u9t2
+ 40253u10t + 3555u
11)s9
+ 3(1100t
12+ 16144u t
11+ 105097u
2t10
+ 356156u3t9
+ 736699u4t8
+ 1061804u5t7
+ 1182566u6t6
+ 1061804u7t5
+ 736699u8t4
+ 356156u9t3
+ 105097 u10t2
+ 16144u11t + 1100u
12)s8
+ 2(471t
13+ 10059u t
12
– 39 –
=+89007u2t11
+370856u3t10
+918809u4t9
+1568172u5t8
+2010976u6t7
+2010976u7t6
+1568172u8t5
+918809u9t4
+370856 u10t3
+ 89007u11t2
+ 10059u12t + 471u
13)s7
+(124 t
14+ 5166ut
13+ 68942u
2t12
+ 360694u3t11
+ 1093775u4t10
+ 2281660u5t9
+ 3515021u6t8
+ 4060864u7t7
+ 3515021u8t6
+ 2281660u9t5
+ 1093775u10t4
+ 360694u11t3
+ 68942u12t2
+ 5166u13t+ 124u
14)s6
+ 6tu(102t
13+ 2718u t
12+ 19299u
2t11
+ 75952u3t10
+ 198691u4t9
+ 370135u5t8
+ 503605u6t7
+ 503605u7t6
+ 370135u8t5
+ 198691u9t4
+ 75952u10
t3
+ 19299u11t2
+ 2718u12t + 102u
13)s5
+ t2u2(1752 t
12+ 21508ut
11+ 127396u
2t10
+ 438996u3t9
+ 986209u4t8
+ 1559032u5t7
+ 1808388u6t6
+ 1559032u7t5
+ 986209u8t4
+ 438996 u9t3
+ 127396u10t2
+ 21508u11t+ 1752u
12)s4
+ 2t3u3(834t
11+ 10755ut
10+ 52845u
2t9
+ 146657u3t8
+ 271322u4t7
+ 363015u5t6
+ 363015u6t5
+ 271322u7t4
+ 146657u8t3
+52845u9t2
+10755u10t+834u
11)s3
+6t4u4(t+u)
2(283 t
8+1733ut
7+4779u
2t6
+8360u3t5
+10092u4t4
+8360u5t3
+4779u6t2
+1733u7t+283u
8)s2
+2t5u5(t+u)
3(282t
6+1178u t
5+2417u
2t4
+3162u3t3
+2417u4t2
+1178u5t+282u
6)s+110 t
6u6(t+u)
4(t2
+ut+u2)2)
H(1, z)H(2, 3, y) + 9s2
(t+u)2(2(20t
8+ 50ut
7+ 21u
2t6 − 82u
3t5 − 102u
4t4 − 82 u
5t3
+ 21u6t2
+ 50u7t+ 20u
8)s16
+ 2(140t
9+ 505u t
8+ 568u
2t7 − 298u
3t6 − 1069u
4t5 − 1069u
5t4 − 298u
6t3
+ 568u7t2
+ 505u8t+ 140u
9)s15
+(880t
10+ 4370ut
9
=+8221u2t8
+4262u3t7−6199u
4t6−10932u
5t5−6199u
6t4
+4262u7t3
+8221 u8t2
+4370u9t+880u
10)s14
+2(820t
11+5395u t
10
+ 14563u2t9
+ 17988u3t8
+ 5650u4t7 − 8508u
5t6 − 8508u
6t5
+ 5650u7t4
+ 17988u8t3
+ 14563u9t2
+ 5395u10t + 820u
11)s13
+(2000t
12+16930ut
11+60889u
2t10
+115200u3t9
+112888u4t8
+52018u5t7
+18062u6t6
+52018u7t5
+112888u8t4
+115200u9t3
+ 60889u10t2
+ 16930u11t + 2000u
12)s12
+ 2(820t
13+ 8825ut
12+ 40630u
2t11
+ 106430u3t10
+ 162506u4t9
+ 145433u5t8
+94054u6t7
+94054u7t6
+145433u8t5
+162506u9t4
+106430u10t3
+40630u11t2
+8825u12t+820 u
13)s11
+(880t
14+12310ut
13
+ 71305u2t12
+ 252860 u3t11
+ 542940u4t10
+ 672624u5t9
+ 495141u6t8
+ 346704u7t7
+ 495141u8t6
+ 672624u9t5
+ 542940u10t4
+ 252860u11t3
+ 71305 u12t2
+ 12310u13t + 880u
14)s10
+ 2(140t
15+ 2785u t
14+ 20491u
2t13
+ 99450u3t12
+ 294436u4t11
+ 490859u5t10
+ 448931u6t9
+ 254956u7t8
+ 254956u8t7
+ 448931u9t6
+ 490859 u10t5
+ 294436u11t4
+ 99450u12t3
+ 20491u13t2
+ 2785u14
t + 140u15)s9
+(40t
16+ 1490ut
15+ 14845u
2t14
+ 102820u3t13
+ 419280u4t12
+ 950788u5t11
+ 1225773u6t10
+ 975710u7t9
+ 743060u8t8
+ 975710u9t7
+ 1225773u10t6
+ 950788u11t5
+ 419280u12t4
+ 102820u13t3
+ 14845u14t2
+ 1490u15t
+ 40u16)s8
+ 2tu(90t
15+ 1540u t
14+ 16932u
2t13
+ 96123u3t12
+ 304282u4t11
+ 583798u5t10
+ 762212u6t9
+ 803305u7t8
+ 803305u8t7
+ 762212u9t6
+ 583798 u10t5
+ 304282u11t4
+ 96123u12t3
+ 16932u13t2
+ 1540u14
t + 90u15)s7
+ t2u2(282t
14
=+6622ut13
+54887u2t12
+264008u3t11
+776536u4t10
+1517240u5t9
+2171441u6t8
+2431080u7t7
+2171441u8t6
+1517240u9t5
+ 776536u10t4
+ 264008 u11t3
+ 54887u12t2
+ 6622u13t + 282u
14)s6
+ 2t3u3(298t
13+ 4418ut
12+ 40731u
2t11
+ 190625u3t10
+ 505964u4t9
+ 877790u5t8
+ 1117090u6t7
+ 1117090u7t6
+ 877790u8t5
+ 505964u9t4
+ 190625u10t3
+ 40731u11t2
+ 4418u12t
+ 298u13)s5
+ t4u4(536t
12+ 16810ut
11+ 131975u
2t10
+ 463360u3t9
+ 936996u4t8
+ 1292362u5t7
+ 1406138u6t6
+ 1292362u7t5
+ 936996 u8t4
+ 463360u9t3
+ 131975u10t2
+ 16810u11t + 536u
12)s4
+ 2t5u5(848t
11+ 13094ut
10+ 64600u
2t9
+ 162207u3t8
+255217u4t7
+298424u5t6
+298424u6t5
+255217u7t4
+162207u8t3
+64600u9t2
+13094u10t+848u
11)s3
+ t6u6(t+u)
2(2062t
8
+ 13122ut7
+ 32971u2t6
+ 48846u3t5
+ 54292u4t4
+ 48846 u5t3
+ 32971u6t2
+ 13122u7t + 2062u
8)s2
+ 4t7u7(t + u)
3(158t
6
+746ut5
+1500u2t4
+1923u3t3
+1500u4t2
+746u5t+158 u
6)s+8t
8u8(t+u)
4(23t
4+45ut
3+67u
2t2
+45u3t+23 u
4))H(3, 2, y)
=−36s2t2u3(t+u)
2(−12t
(4t
2+7 ut+4u
2)s16−
(413t
4+1112ut
3+1066u
2t2
+344u3t−23 u
4)s15−3
(549t
5+2080ut
4+2910u
2t3
+ 1760u3t2
+ 293 u4t− 64u
5)s14 −
(3849t
6+ 19818ut
5+ 38435u
2t4
+ 35276 u3t3
+ 14007u4t2
+ 482u5t− 715u
6)s13 −
(5797t
7
+ 40039u t6
+ 104248u2t5
+ 133574u3t4
+ 86245u4t3
+ 21235u5t2 − 2834u
6t− 1572u
7)s12 − 3
(1839t
8+ 18438ut
7+ 63926u
2t6
+ 107954 u3t5
+ 97302u4t4
+ 43534u5t3
+ 4746u6t2 − 2870u
7t− 757u
8)s11 −
(2469t
9+ 52233ut
8+ 250929u
2t7
+ 546879u3t6
+ 638973u4t5
+ 405133u5t4
+ 113599u6t3− 8307u
7t2− 12530u
8t− 2258u
9)s10
+(985t
10− 31352ut9− 228083u
2t8− 646444u
3t7
− 969791u4t6− 819288u
5t5− 357472u
6t4− 38248u
7t3
+ 28876u8t2
+ 11404u9t+ 1557u
10)s9
+ 3(727t
11− 3289ut10− 45068u
2t9
−168873u3t8−330122u
4t7−375394u
5t6−241202u
6t5−66685u
7t4
+10259u8t3
+10981u9t2
+2326u10t+240u
11)s8
+(1386t
12
−6ut11−44480u
2t10−241022u
3t9−645063u
4t8−1001980u
5t7−922078u
6t6−455700u
7t5−58195u
8t4
+50450u9t3
+22836u10t2
+ 2866u11t + 202u
12)s7
+(420 t
13+ 1149ut
12+ 3u
2t11 − 48559u
3t10 − 253354u
4t9 − 575952u
5t8 − 717884u
6t7 − 512534u
7t6
−180305u8t5
+7313u9t4
+31999u10t3
+10093u11t2
+729u12t+26u
13)s6
+3t(16 t
13+94ut
12+2346u
2t11
+5138u3t10−15062u
4t9
− 74024u5t8 − 122999u
6t7 − 106460u
7t6 − 49523u
8t5 − 8048u
9t4
+ 4593u10t3
+ 3534u11t2
+ 893u12t+ 30u
13)s5
+ t2u(− 6 t
12
+ 2684ut11
+ 12044u2t10
+ 7299u3t9 − 50331u
4t8 − 127806u
5t7 − 131304u
6t6 − 58843u
7t5
+ 1403u8t4
+ 13260u9t3
+ 6238u10t2
+ 1774u11t + 336u
12)s4
+ 2t3u2(166t
11+ 1146u t
10+ 2486u
2t9 − 448u
3t8 − 9790u
4t7 − 15423u
5t6 − 8416u
6t5
+ 3041 u7t4
– 40 –
= + 7002u8t3
+ 4035u9t2
+ 960u10t+ 57u
11)s3
+ 3t4u3(t+ u)
2(15t
8+ 240ut
7+ 369u
2t6 − u3
t5 − 172u
4t4
+ 126u5t3
+ 429u6t2
+ 355u7t+ 103u
8)s2
+ t5u4(t+u)
3(90 t
6+ 272ut
5+ 116u
2t4
+ 114u3t3
+ 135u4t2
+ 117u5t+ 66u
6)s+ t
6u5(t+u)
4(11t
4− 2ut3
+ 15u2t2
+ 14u3t+ 19 u
4))H(0, 0, 1, z) + 18s
2t2(s+ t)
2u2(2(55t
6+ 282 ut
5+ 849u
2t4
+ 834u3t3
+ 876u4t2
+ 306u5t+ 62u
6)s14
+ 2(330t
7+ 2024ut
6+ 6897u
2t5
+ 10755u3t4
+ 10754u4t3
+ 8154u5t2
+ 2583u6t+ 471u
7)s13
+ 2(935t
8+ 6797ut
7+ 25584u
2t6
+ 52845u3t5
+ 63698u4t4
+ 57897u5t3
+ 34471u6t2
+ 10059u7t+ 1650 u
8)s12
+ 2(1650t
9+ 14229ut
8+ 58953u
2t7
+ 146657u3t6
+219498u4t5
+227856u5t4
+180347u6t3
+89007u7t2
+24216u8t+3555u
9)s11
+(3960t
10+40664ut
9+189546u
2t8
+542644 u3t7
+ 986209u4t6
+ 1192146u5t5
+ 1093775u6t4
+ 741712u7t3
+ 315291 u8t2
+ 80506u9t + 10571u
10)s10
+ 2(1650t
11+ 20332u t
10
+ 110712u2t9
+ 363015u3t8
+ 779516u4t7
+ 1110405u5t6
+ 1140830 u6t5
+ 918809u7t4
+ 534234u8t3
+ 202415u9t2
+ 48730u10t
+ 5736 u11)s9
+(1870t
12+ 28458ut
11+ 189546u
2t10
+ 726030 u3t9
+ 1808388u4t8
+ 3021630u5t7
+ 3515021u6t6
+ 3136344u7t5
+ 2210097u8t4
+ 1122420u9t3
+ 390525u10t2
+ 88182u11t + 9297 u
12)s8
+ 2(330t
13+ 6797ut
12+ 58953u
2t11
+ 271322 u3t10
+779516u4t9
+1510815u5t8
+2030432u6t7
+2010976u7t6
+1592706u8t5
+989305u9t4
+447975u10t3
+144438u11t2
+29896 u12t
+ 2795u13)s7
+(110t
14+ 4048ut
13+ 51168u
2t12
+ 293314u3t11
+ 986209u4t10
+ 2220810u5t9
+ 3515021u6t8
+ 4021952u7t7
= + 3547698u8t6
+ 2514596u9t5
+ 1372200u10t4
+ 555762u11t3
+ 162893u12t2
+ 29722u13t+ 2385u
14)s6
+ 2u(282t
14+ 6897ut
13
+52845u2t12
+219498u3t11
+596073u4t10
+1140830u5t9
+1568172u6t8
+1592706u7t7
+1257298u8t6
+780186u9t5
+369966u10t4
+ 132928u11t3
+ 34077 u12t2
+ 5151u13t + 323u
14)s5
+ u2(1698t
14+ 21510u t
13+ 127396u
2t12
+ 455712u3t11
+ 1093775u4t10
+ 1837618u5t9
+ 2210097u6t8
+ 1978610u7t7
+ 1372200u8t6
+ 739932u9t5
+ 307366 u10t4
+ 96362u11t3
+ 20205u12t2
+ 2236u13t
+ 83u14)s4
+ 2tu3(834t
13+ 10754ut
12+ 57897u
2t11
+ 180347u3t10
+ 370856u4t9
+ 534234u5t8
+ 561210u6t7
+ 447975u7t6
+ 277881 u8t5
+ 132928u9t4
+ 48181u10t3
+ 12378u11t2
+ 1869u12t+ 112 u
13)s3
+ t2u4(t+u)
2(1752t
10+ 12804ut
9+ 41582u
2t8
+ 82046u3t7
+ 109617u4t6
+ 103550u5t5
+ 73808u6t4
+ 37710u7t3
+ 13665u8t2
+ 3114u9t + 312u
10)s2
+ 2t3u5(t + u)
3(306t
8
+ 1665ut7
+ 4146u2t6
+ 6477u3t5
+ 6719u4t4
+ 4996u5t3
+ 2469u6t2
+ 782u7t+ 112u
8)s+ t
4u6(t+u)
6(124 t
4+ 198ut
3+ 252u
2t2
+ 148u3t + 83u
4))H(0, 1, 0, y)− 18s
2t2u2(t + u)
3(2t(7t
2+ 15ut + 12u
2)s16
+ 12(8 t
4+ 24ut
3+ 29u
2t2
+ 12u3t− u4
)s15
+ 3(101t
5+ 423u t
4+ 720u
2t3
+ 556u3t2
+ 111u4t− 31u
5)s14
+(598 t
6+ 3066ut
5+ 7134u
2t4
+ 8992u3t3
+ 5154u4t2
+ 510u5t
− 318 u6)s13
+(851t
7+ 4495ut
6+ 13290u
2t5
+ 25506u3t4
+ 26949 u4t3
+ 12309u5t2
+ 688u6t− 652u
7)s12
+ 6(158t
8+ 586u t
7
+ 2628u2t6
+ 7708u3t5
+ 11649u4t4
+ 9092u5t3
+ 3324u6t2
+ 218 u7t− 155u
8)s11
+(851t
9 − 417ut8
+ 9564u2t7
+ 62150u3t6
= + 123813u4t5
+ 121269u5t4
+ 67982u6t3
+ 23208u7t2
+ 2838u8t− 1002u
9)s10
+ 2(299t
10 − 2075ut9 − 1896u
2t8
+ 23751 u3t7
+ 72903u4t6
+ 97515u5t5
+ 71423u6t4
+ 31963u7t3
+ 10800u8t2
+ 1966u9t− 409u
10)s9
+ 3(101t
11 − 1463ut10 − 3896 u
2t9
+208u3t8
+20429u4t7
+58669u5t6
+80268u6t5
+55172u7t4
+19400u8t3
+4832u9t2
+1000u10t−156u
11)s8
+2(48t
12−1128ut11
− 4410u2t10 − 17090u
3t9 − 31983u
4t8
+ 6084u5t7
+ 100874u6t6
+ 143160u7t5
+ 88338u8t4
+ 23800u9t3
+ 2622u10t2
+ 582u11t
− 81u12)s7
+(14t
13 − 572u t12 − 3036u
2t11 − 35818u
3t10 − 106376u
4t9 − 101688u
5t8
+ 48822 u6t7
+ 213630u7t6
+ 239397u8t5
+134809u9t4
+31274u10t3−36 u
11t2
+157u12t−25u
13)s6−6tu
(8t
12+37u t
11+3213u
2t10
+11984u3t9
+14592u4t8
+1987u5t7
− 12914u6t6 − 20563u
7t5 − 20499u
8t4 − 11612u
9t3 − 2423u
10t2
+ 147u11t + 3 u
12)s5
+ t2u2(102t
11 − 5234ut10 − 25530u
2t9
− 39126 u3t8 − 12408u
4t7
+ 24648u5t6
+ 35505u6t5
+ 40505u7t4
+ 40476u8t3
+ 21240u9t2
+ 3629u10t− 267u
11)s4
+ 2t3u3(
− 266 t10 − 1804ut
9 − 4752u2t8 − 4830u
3t7
+ 378u4t6
+ 5301u5t5
+ 6806 u6t4
+ 6178u7t3
+ 3642u8t2
+ 1119u9t + 156u
10)s3
+ 3t4u4
(t + u)2(16t
7 − 382ut6 − 532u
2t5
+ 8u3t4
+ 467u4t3
+ 637u5t2
+ 265u6t− 71u
7)s2 − 2t
5u5(t + u)
3(48t
5+ 151ut
4
− 84 u2t3
+ 18u3t2 − 160u
4t− 15u
5)s + t
6u7(t + u)
3(12t
3+ 3 ut
2+ 2u
2t− 11u
3))H(0, 3, 2, y)− 18s
2t2u2(t + u)
2((
55t4
= + 148ut3
+ 192u2t2
+ 128u3t+ 47u
4)s16
+ 2(232t
5+ 807ut
4+ 1262u
2t3
+ 1126u3t2
+ 612u4t+ 173u
5)s15
+ 6(305t
6+ 1324ut
5
+ 2458u2t4
+ 2648u3t3
+ 1862u4t2
+ 872 u5t + 201u
6)s14
+ 2(2230t
7+ 11932ut
6+ 26409u
2t5
+ 33217 u3t4
+ 27682u4t3
+ 16830u5t2
+ 7005u6t+ 1347u
7)s13
+(7450t
8+ 48274ut
7+ 129744u
2t6
+ 195540u3t5
+ 190555u4t4
+ 134098u5t3
+ 72590u6t2
+ 26532u7t + 4375u
8)s12
+ 6(1486t
9+ 11488ut
8+ 37756u
2t7
+ 69937u3t6
+ 82622u4t5
+ 67718 u5t4
+ 41832u6t3
+ 19931u7t2
+ 6288u8t+ 910u
9)s11
+(7744t
10+ 71242ut
9+ 290076u
2t8
+ 661446u3t7
+ 946629 u4t6
+ 926538u5t5
+ 671989u6t4
+ 379294u7t3
+ 157923u8t2
+ 41472 u9t + 5271u
10)s10
+ 2(2410t
11+ 26794ut
10+ 138966 u
2t9
+ 391138u3t8
+ 666867u4t7
+ 763472u5t6
+652628u6t5
+448145 u7t4
+237429u8t3
+84416u9t2
+17568u10t+1903u
11)s9
+3(685t
12+9638ut
11+66160u
2t10
+229988u3t9
+ 468878u4t8
+ 632074u5t7
+ 626493u6t6
+ 499908u7t5
+ 326013u8t4
+ 156448u9t3
+ 46699u10t2
+ 7420u11t + 638u
12)s8
+ 2(270 t
13+ 5385ut
12+ 51810u
2t11
+ 219533u3t10
+ 538700u4t9
+ 893700u5t8
+ 1082558u6t7
+ 993074u7t6
+ 712998u8t5
+405820u9t4
+169330u10t3
+42843u11t2
+4984u12t+295u
13)s7
+(66t
14+2518ut
13+38032u
2t12
+195010u3t11
+579501 u4t10
– 41 –
=+1219748u5t9
+1901521u6t8
+2145380u7t7
+1729402u8t6
+1029790u9t5
+480198u10t4
+170114u11t3
+36457u12t2
+2808u13t
+83u14)s6
+6tu(46t
13+1463u t
12+9551u
2t11
+36573u3t10
+99722u4t9
+196920u5t8
+275717 u6t7
+269768u7t6
+184750u8t5
+90822u9t4
+33632u10t3
+9403 u11t2
+1592u12t+61u
13)s5
+ t2u2(936t
12+9592 ut
11+58498u
2t10
+216504u3t9
+517783u4t8
+ 852472u5t7
+ 999621u6t6
+ 842754u7t5
+ 506934u8t4
+ 212352u9t3
+ 59561u10
t2
+ 10778u11t + 1137u
12)s4
+ 2t3u3(306t
11
+ 5120u t10
+ 27107u2t9
+ 77806u3t8
+ 147341u4t7
+ 200386u5t6
+ 201078u6t5
+ 148590u7t4
+ 78861u8t3
+ 28022u9t2
+ 5655u10t
+ 424 u11)s3
+ 3t4u4(t+u)
2(312t
8+ 1862ut
7+ 5114u
2t6
+ 9264u3t5
+ 11523u4t4
+ 9432u5t3
+ 5226u6t2
+ 1942u7t+ 361 u
8)s2
+ 2t5u5(t+ u)
3(138t
6+ 635ut
5+ 1406u
2t4
+ 1938 u3t3
+ 1431u4t2
+ 633u5t+ 159u
6)s+ 3t
6u6(t+ u)
4(22 t
4+ 48ut
3+ 71u
2t2
+46u3t+23u
4))H(1, 0, 1, z)−18s
2t2
(s+t)3u2((
11t6−30ut
5+213u
2t4−312u
3t3
+267u4t2
+18u5t+25u
6)s13
+(31t
7−410ut6
−369u2t5−2238 u
3t4−3629u
4t3
+ 882u5t2−157u
6t+ 162u
7)s12
+ 6(4 t
8−169ut7−548u
2t6−1214u
3t5−3540u
4t4−2423u
5t3
+6u6t2−194u
7t+78u
8)s11−2
(8t
9+525ut
8+3009u
2t7
+6178 u3t6
+20238u4t5
+34836u5t4
+15637u6t3
+2622u7t2
+1500u8t
−409u9)s10−
(47t
10+414ut
9+4737u
2t8
+13612u3t7
+40505u4t6
+122994u5t5
+134809u6t4
+47600u7t3
+14496u8t2
+3932u9t
−1002u10)s9−3
(13t
11−178ut10−49u
2t9
+3534u3t8
+11835u4t7
+41126u5t6
+79799u6t5
+58892u7t4
+19400u8t3
+7200u9t2
= + 946u10t− 310u
11)s8 − 2
(6 t
12 − 513ut11 − 2157u
2t10
+ 378u3t9
+ 12324u4t8
+ 38742u5t7
+ 106815u6t6
+ 143160u7t5
+ 82758u8t4
+ 31963u9t3
+ 11604u10
t2
+ 654u11t− 326u
12)s7
+ 2u(295t
12+ 1920u t
11+ 4830u
2t10
+ 6204u3t9
+ 5961u4t8
− 24411u5t7 − 100874u
6t6 − 120402u
7t5 − 71423u
8t4 − 33991u
9t3 − 9972u
10t2 − 344u
11t + 159u
12)s6
+ 3u(32t
13+ 350ut
12
+ 3168u2t11
+ 13042u3t10
+ 29184u4t9
+ 33896u5t8 − 4056u
6t7 − 58669u
7t6 − 65010u
8t5 − 40423u
9t4 − 18184u
10t3
− 4103u11t2 − 170u
12t+ 31u
13)s5
+ u2(− 48t
13+ 3608ut
12+ 25530u
2t11
+ 71904u3t10
+ 106376u4t9
+ 63966u5t8 − 61287u
6t7
− 145806 u7t6− 123813u
8t5− 69894u
9t4− 26949u
10t3− 5154u
11t2− 333 u
12t+ 12u
13)s4
+ 2tu3(266t
12+ 2617ut
11+ 9639 u
2t10
+ 17909u3t9
+ 17090u4t8 − 312u
5t7 − 23751u
6t6 − 31075u
7t5 − 23124u
8t4 − 12753u
9t3 − 4496u
10t2 − 834u
11t− 72 u
12)s3
− 6tu4(t + u)
2(17t
10 − 71ut9 − 381u
2t8 − 637 u
3t7 − 293u
4t6
+ 591u5t5
+ 705u6t4
+ 627u7t3
+ 256u8t2
+ 50u9t + 4u
10)s2
+ t2u5(t + u)
3(48t
8+ 428ut
7+ 828u
2t6
+ 573 u3t5 − 481u
4t4 − 687u
5t3 − 585u
6t2 − 198u
7t− 30u
8)s− t3 u6
(t + u)6(14t
4
+ 12ut3
+ 21u2t2
+ 12u3t + 14u
4))
H(2, 1, 0, y)− 18s2t2u2(t + u)
2((
83t4
+ 224ut3
+ 312u2t2
+ 224u3t + 83u
4)s16
+(646t
5
+ 2236ut4
+ 3738u2t3
+ 3738u3t2
+ 2236u4t + 646u
5)s15
+ 3(795t
6+ 3434u t
5+ 6735u
2t4
+ 8252u3t3
+ 6735u4t2
+ 3434u5t
+ 795u6)s14
+(5590t
7+ 29722ut
6+ 68154u
2t5
+ 96362u3t4
+ 96362u4t3
+ 68154u5t2
+ 29722u6t + 5590u
7)s13
+(9297t
8
= + 59792u t7
+ 162893u2t6
+ 265856u3t5
+ 307366u4t4
+ 265856u5t3
+ 162893u6t2
+ 59792u7t + 9297u
8)s12
+ 6(1912t
9
+ 14697ut8
+ 48146 u2t7
+ 92627u3t6
+ 123322u4t5
+ 123322u5t4
+ 92627u6t3
+ 48146u7t2
+ 14697u8t + 1912u
9)s11
+(10571t
10+ 97460ut
9+ 390525 u
2t8
+ 895950u3t7
+ 1372200u4t6
+ 1560372u5t5
+ 1372200u6t4
+ 895950u7t3
+ 390525u8t2
+ 97460u9t + 10571u
10)s10
+ 2(3555t
11+ 40253ut
10+ 202415u
2t9
+ 561210u3t8
+ 989305u4t7
+ 1257298u5t6
+ 1257298u6t5
+ 989305u7t4
+ 561210u8t3
+ 202415u9t2
+ 40253u10t + 3555u
11)s9
+ 3(1100t
12+ 16144u t
11+ 105097u
2t10
+ 356156u3t9
+ 736699u4t8
+ 1061804u5t7
+ 1182566u6t6
+ 1061804u7t5
+ 736699u8t4
+ 356156u9t3
+ 105097 u10t2
+ 16144u11t+ 1100u
12)s8
+ 2(471t
13+ 10059u t
12+ 89007u
2t11
+ 370856u3t10
+ 918809u4t9
+ 1568172u5t8
+ 2010976u6t7
+ 2010976u7t6
+ 1568172u8t5
+ 918809u9t4
+ 370856 u10t3
+ 89007u11t2
+ 10059u12t + 471u
13)s7
+(124 t
14+ 5166ut
13+ 68942u
2t12
+ 360694u3t11
+ 1093775u4t10
+ 2281660u5t9
+ 3515021u6t8
+ 4060864u7t7
+ 3515021u8t6
+ 2281660u9t5
+ 1093775u10t4
+ 360694u11t3
= + 68942u12
t2
+ 5166u13t + 124u
14)s6
+ 6tu(102t
13+ 2718u t
12+ 19299u
2t11
+ 75952u3t10
+ 198691u4t9
+ 370135u5t8
+ 503605u6t7
+ 503605u7t6
+ 370135u8t5
+ 198691u9t4
+ 75952u10
t3
+ 19299u11t2
+ 2718u12t + 102u
13)s5
+ t2u2(1752 t
12
+ 21508ut11
+ 127396u2t10
+ 438996u3t9
+ 986209u4t8
+ 1559032u5t7
+ 1808388u6t6
+ 1559032u7t5
+ 986209u8t4
+ 438996 u9t3
+ 127396u10t2
+ 21508u11t + 1752u
12)s4
+ 2t3u3(834t
11+ 10755ut
10+ 52845u
2t9
+ 146657u3t8
+ 271322u4t7
+ 363015u5t6
+ 363015u6t5
+ 271322u7t4
+ 146657u8t3
+ 52845u9t2
+ 10755u10t + 834u
11)s3
+ 6t4u4(t + u)
2(283 t
8+ 1733ut
7+ 4779u
2t6
+ 8360u3t5
+ 10092u4t4
+ 8360u5t3
+ 4779u6t2
+ 1733u7t+ 283u
8)s2
+ 2t5u5(t+ u)
3(282t
6+ 1178u t
5+ 2417u
2t4
+ 3162u3t3
+ 2417u4t2
+ 1178u5t + 282u
6)s + 110 t
6u6(t + u)
4(t2
+ ut + u2)2)
H(2, 3, 2, y)
}/(27s
3t3u3(s + t)
6(s + u)
6(t + u)
6)
– 42 –
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Recommended